Gabriel Navarro

Department of Algebra
University of Granada

At present, I am a professor (Catedrático de Universidad) at the Department of Algebra of the University of Granada. Prior to this, from 2007 until 2023, I was within the Department of Computer Sciences and AI.

Foto de Gabriel Navarro

Research interests

Representation Theory of (Co)algebras

Non-commutative Localization

Non-commutative Geometry

Fuzzy/Rough/Soft Sets Theory

Approximate Reasoning

Symbolic Computation

Coding Theory

Quantum Machine Learning

Post-Quantum Cryptography

Publications

Phd Thesis. Representation Theory of Coalgebras. Localization in coalgebras, January 2006, pdf file (revised version, 2007). Frontpage image, jpg file

  1. P. Jara, L. Merino, Gabriel Navarro and E. Santos, On gradual sets, set-valued fuzzy sets and representation theorems, IEEE Access 12 (2024), 111158-111168. 10.1109/ACCESS.2024.3441940
  2. E. Andrés, M. P. Cuéllar, and Gabriel Navarro, Brain-inspired agents for quantum reinforcement learning, Mathematics 128(8) (2024), 1230. 10.3390/math12081230
  3. A. Y. Darani, Y. Khedmati, H. Pakmanesh and Gabriel Navarro, Image encryption algorithm based on a new 3D chaotic system using cellular automata, Chaos, Solitons and Fractals 179 (2024), article 114396. 10.1016/j.chaos.2023.114396
  4. A. Y. Darani, Y. Khedmati, Gabriel Navarro, H. Pakmanesh and J. Sharafi, Optimal location using genetic algorithms for chaotic image steganography technique based on discrete framelet transform, Digital Signal Processing 144 (2024), article 104228. 10.1016/j.dsp.2023.104228
  5. E. Andrés, M. P. Cuéllar, and Gabriel Navarro, Efficient dimensionality reduction strategies for quantum reinforcement learning, IEEE Access 11 (2023), 104534-104553. 10.1109/ACCESS.2023.3318173
  6. J. Gómez-Torrecillas, F.J. Lobillo, and Gabriel Navarro, Skew differential Goppa codes and their application to McEliece cryptosystem, Designs, codes and cryptography 91 (2023), 3995–4017. 10.1007/s10623-023-01286-6
  7. P. Jara, L. Merino, Gabriel Navarro and E. Santos, A lattice structure on hesitant fuzzy sets, IEEE Transactions on Fuzzy Systems 31(6) (2023), 2018-2028. 10.1109/TFUZZ.2022.3217400
  8. M.P. Cuéllar, J. Lobillo and Gabriel Navarro, Fast parallel computation of reduced row echelon form to find the minimum distance of linear codes, Expert Systems with Applications 224 (2023), article 119955. 10.1016/j.eswa.2023.119955
  9. E. Andrés, M. P. Cuéllar, and Gabriel Navarro, On the use of Quantum Reinforcement Learning in energy efficiency scenarios, Energies 15(16) 2022, 6034. 10.3390/en15166034
  10. L. Merino, Gabriel Navarro and E. Santos, Induced operators on bounded lattices, Information Sciences 608 (2022), 114-136. 10.1016/j.ins.2022.06.033
  11. C. Gutiérrez-Braojos, C. Rodríguez-Domínguez, F. Carranza-García and G. Navarro-Garulo, Computer supported knowledge building community: A new learning analytics tool, in: Remote Learning in Times of Pandemic. Issues, Implications and Best Practice, edited by Linda Daniela and Anna Visvizi, Routledge Research in Digital Education and Educational Technology Series, Routledge (Taylor and Francis Group), 2022, pp. 35-50.10.4324/9781003167594
  12. J. Gómez-Torrecillas, P. Kutas, F. J. Lobillo and Gabriel Navarro, Primitive idempotents in central simple algebras over F_q(t) with an application to coding theory, Finite Fields and Their Applications 77 (2022), article 101935. 10.1016/j.ffa.2021.101935
  13. J. Gómez-Torrecillas, Gabriel Navarro and J. P. Sánchez-Hernández, Decoding Reed-Solomon Skew-Differential Codes, IEEE Transactions on Information Theory 67 (12) (2021), 7891-7903.10.1109/TIT.2021.3117083
  14. J. Gómez-Torrecillas, J. Lobillo and Gabriel Navarro, Decoding linear codes over chain rings given by parity check matrices, Mathematics 9(16) 2021, article 1878. 10.3390/math9161878
  15. F.J. Lobillo, L. Merino, Gabriel Navarro and E. Santos, Induced triangular norms and negations on bounded lattices, IEEE Transactions on Fuzzy Systems 29(7) 2021, 1802-1814. 10.1109/TFUZZ.2020.2985337
  16. J. Gómez-Torrecillas, F. J. Lobillo, Gabriel Navarro and J. P. Sánchez-Hernández, Peterson-Gorenstein-Zierler algorithm for differential convolutional codes, Applicable Algebra in Engineering, Communication and Computing 32 (2021), 321-344. 10.1007/s00200-020-00464-6
  17. M. P. Cuéllar, J. Gómez-Torrecillas, F. J. Lobillo and Gabriel Navarro, Genetic algorithms with permutation-based representation for computing the distance of linear codes, Swarm and Evolutionary Computation 60 (2021), 100797. 10.1016/j.swevo.2020.100797
  18. J. Gómez-Torrecillas, F. J. Lobillo and Gabriel Navarro, Biseparable extensions are not necessarily Frobenius, Mathematische Zeitschrift 297 (2021), 517-533. 10.1007/s00209-020-02523-7
  19. J. Gómez-Torrecillas, F. J. Lobillo and Gabriel Navarro, Cyclic Distances of Idempotent Convolutional Codes, Journal of Symbolic Computation 102 (2021), 37-62. 10.1016/j.jsc.2019.10.008
  20. J. Gómez-Torrecillas, E. Hieta-Aho, F. J. Lobillo , S. López-Permouth, Gabriel Navarro, Some remarks on non projective Frobenius algebras and linear codes, Designs, Codes and Cryptography 88 (2020), 1-15. 10.1007/s10623-019-00666-1
  21. J. Gómez-Torrecillas, F.J. Lobillo and Gabriel Navarro, Dual skew codes from annihilators: Transpose Hamming ring extensions, In: Rings, Modules and Codes, 131-148, Contemporary Mathematics 727, American Mathematical Society, Providence, RI, 2019. 10.1090/conm/727
  22. J. Gómez-Torrecillas, F.J. Lobillo, and Gabriel Navarro, Computing the bound of an Ore polynomial. Applications to factorization, Journal of Symbolic Computation 92 (2019), 269-297. 10.1016/j.jsc.2018.04.018
  23. J. Gómez-Torrecillas, F.J. Lobillo and Gabriel Navarro, Minimum distance computation of linear codes via genetic algorithms with permutation encoding, ACM Communications in Computer Algebra 52(3) (2018), 71-74. 10.1145/3313880.3313886
  24. F.J. Lobillo, L. Merino, Gabriel Navarro and E. Santos, Embeddings between lattices of fuzzy sets: an application of closed-valued fuzzy sets, Fuzzy Sets and Systems 352 (2018), 56-72. 10.1016/j.fss.2018.04.014
  25. J. Gómez-Torrecillas, F.J. Lobillo, and Gabriel Navarro, Computing free distances of idempotent convolutional codes, In Proceedings of the 43rd International Symposium on Symbolic and Algebraic Computation (ISSAC '18), 175-182, ACM, New York, NY, USA. 10.1145/3208976.3208985
  26. J. Gómez-Torrecillas, F.J. Lobillo, Gabriel Navarro and A. Neri, Hartmann-Tzeng bound and skew cyclic codes of designed Hamming distance, Finite Fields and Their Applications 50 (2018), 84-112. 10.1016/j.ffa.2017.11.001
  27. J. Gómez-Torrecillas, F.J. Lobillo, and Gabriel Navarro, Peterson-Gorenstein-Zierler algorithm for skew RS codes, Linear and Multilinear Algebra 66 (2018), 469-487. 10.1080/03081087.2017.1301364
  28. J. Gómez-Torrecillas, F.J. Lobillo, and Gabriel Navarro, A Sugiyama-like decoding algorithm for convolutional codes, IEEE Transactions on Information Theory 63 (2017) 6216-6226.10.1109/TIT.2017.2731774
  29. J. Gómez-Torrecillas, F.J. Lobillo, and Gabriel Navarro, Ideal codes over separable ring extensions, IEEE Transactions on Information Theory 65 (2017), 2796-2813. 10.1109/TIT.2017.2682856
  30. J. Gómez-Torrecillas, F.J. Lobillo, and Gabriel Navarro, Computing separability elements for the sentence–ambient algebra of split ideal codes, Journal of Symbolic Computation 83 (2017), 211-227. http://doi.org/10.1016/j.jsc.2016.11.012
  31. J. Gómez-Torrecillas, F.J. Lobillo, and Gabriel Navarro, A new perspective of cyclicity in convolutional codes, IEEE Transactions on Information Theory 62 (5) (2016), 2702-2706. 10.1109/TIT.2016.2538264
  32. F.J. Lobillo, L. Merino, Gabriel Navarro and E. Santos, Rough ideals under relations associated to fuzzy ideals, Information Sciences 352-353 (2016), 121-132. http://doi.org/10.1016/j.ins.2016.02.058
  33. J. Gómez-Torrecillas, F. J. Lobillo and Gabriel Navarro, An isomorphism test for modules over a non-commutative PID. Applications to similarity of Ore polynomials, Journal of Symbolic Computation 75 (2016), 149-170. 10.1016/j.jsc.2015.11.012
  34. J. Gómez-Torrecillas, F. J. Lobillo and Gabriel Navarro, Convolutional codes with a matrix-algebra word-ambient, Advances in Mathematics of Communication 10 (2016), 29-43. 10.3934/amc.2016.10.29
  35. J. Gómez-Torrecillas, F. J. Lobillo and Gabriel Navarro, Separability test and cyclic convolutuonal codes, in: XV Encuentro de Álgebra Computacional y Aplicaciones: EACA 2016, pp. 93-96. Ed: J. Heras and A. Romero, Logroño, 2014. Published by Universidad de La Rioja. ISBN 978-84-608-9024-9.Dialnet
  36. J. Gómez-Torrecillas, F. J. Lobillo and Gabriel Navarro, Information-bit error rate and false positives in an MDS code, Advances in Mathematics of Communication 9 (2015), 149-168. 10.3934/amc.2015.9.149
  37. J. Gómez-Torrecillas, F. J. Lobillo and Gabriel Navarro, Cyclic convolutional codes over separable extensions, in Coding Theory and Applications (eds. R. Pinto, P. R. Malonek and P. Vettori), CIM Series in Mathematical Sciences, Springer, 2015. 10.1007/978-3-319-17296-5_22
  38. J. Gómez-Torrecillas, F.J. Lobillo and Gabriel Navarro, Separable automorphisms on matrix algebras over finite field extensions: applications to ideal codes, in Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation (ISSAC '15). ACM, New York, NY, USA, 189-195. 10.1145/2755996.2756671
  39. J. Gómez-Torrecillas, F.J. Lobillo and Gabriel Navarro, Generating idempotents in ideal codes, ACM Communications in Computer Algebra 48 (3/4) (2014), 113-115. 10.1145/2733693.2733703
  40. J. Gómez-Torrecillas, F.J. Lobillo and Gabriel Navarro, On isomorphisms of modules over non-commutative PDI, in Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation (ISSAC '14), Katsusuke Nabeshima (Ed.). ACM, New York, NY, USA, 210-216. 10.1145/2608628.2608665
  41. J. Gómez-Torrecillas, F.J. Lobillo and Gabriel Navarro, A similarity test for Ore polynomials, in: XIV Encuentro de Álgebra Computacional y Aplicaciones, pp. 123-126. Ed: J. Elias, J. Fernández-Sánchez, and M. Sombra, Barcelona, 2014. ISBN 978-84-697-0651-0. Dialnet
  42. Gabriel Navarro, The valued Gabriel quiver of a wedge product and semiprime coalgebras, Front. Math. China 8 (2013), 1157--1183. 10.1007/s11464-013-0310-19
  43. Gabriel Navarro, O. Cortadellas and F. J. Lobillo, Prime fuzzy ideals over noncomutative rings, Fuzzy Sets and Systems 199 (2012), 108-120. 10.1016/j.fss.2011.11.002
  44. P. Jara, J. López Peña, Gabriel Navarro and D. Stefan, On the classification of twisting maps between K^n and K^m, Algebr. Reprensent. Theory 14 (2011), 869-895. 10.1007/s10468-010-9222-x
  45. O. Cortadellas, J. López Peña and Gabriel Navarro, Factorization structures with a 2-dimensional factor, J. London Math. Soc 81 (2010), 1-23. 10.1112/jlms/jdp055
  46. P. Jara, L. Merino, Gabriel Navarro and J.F. Ruíz, Prime path coalgebras, Arab. J. Sci. Eng. 33 (2008), Number 2C, 273-283. arxiv link
  47. J. Gómez-Torrecillas and Gabriel Navarro, Serial coalgebras and their valued Gabriel quivers, J. Algebra 319 (2008), 5039-5059. 10.1016/j.jalgebra.2008.03.020
  48. J. López Peña and Gabriel Navarro, On the classification and properties of noncommutative duplicates, K-Theory 38 (2008), 223-234. 10.1007/s10977-007-9017-y
  49. Gabriel Navarro, Some remarks on localization in coalgebras, Comm. Algebra 36 (2008), 3447-3466. 10.1080/00927870802107868
  50. R. M. Ibañez Cobos, J. López Peña and Gabriel Navarro, A note on generalized path algebras, Rev. Roumaine Math. Pures Appl. 53(1) (2008), 25-36. Rrc8_1
  51. Gabriel Navarro, Simple comodules and localization in coalgebras, in: Contactforum New techniques in Hopf algebras and graded ring theory, KVAB 2007, 145-164.
  52. P. Jara, L. M. Merino and Gabriel Navarro, Localization in tame and wild coalgebras, J. Pure Appl. Algebra 211 (2007), 342-359. 10.1016/j.jpaa.2007.01.009
  53. P. Jara, L. M. Merino, Gabriel Navarro and F. Ruiz, Localization in coalgebras. Stable localizations and path coalgebras, Comm. Algebra 34 (2006), 2843-2856. 10.1080/00927870802107868
  54. P. Jara, L. M. Merino and Gabriel Navarro, On path coalgebras of quivers with relations, Colloq. Math. 102 (2005), 49-65. 10.4064/cm102-1-5

Manuscripts under consideration

  1. J. Gómez-Torrecillas, F.J. Lobillo, Gabriel Navarro and P. Santonastaso, Adjoint and duality for rank-metric codes in a skew polynomial framework, 2025.
  2. Y. Khedmati, G. Ghasemi, A. Y. Darani and Gabriel Navarro, A comprehensive method for multi-image encryption by a designed scrambling method and twin enhanced logistic maps, 2025.
  3. L. Merino, Gabriel Navarro, C. Salvatierra and E. Santos, An order-oriented approach to scoring hesitant fuzzy elements, 2025.
  4. J. Gómez-Torrecillas, F.J. Lobillo, and Gabriel Navarro, A knapsack McEliece-based public key cryptosystem, 2024.
  5. E. Andrés, M. P. Cuéllar, and Gabriel Navarro, Brain-inspired for enhanced patter recognition: Unifying Quantum Spiking Neural Networks, 2024.

Others

  1. J. López Peña and G. Navarro, Quantum duplicates of algebras, 8 pages, 2007.
  2. J. Gómez-Torrecillas, F.J. Lobillo, and G. Navarro, Factoring Ore polynomials over $\mathbb{F}_q(t)$ is difficult, arxiv link

Posters

  1. J. Gómez-Torrecillas, F. J. Lobillo and G. Navarro, Minimum distance computation of linear codes via genetic algorithms with permutation encoding, in the 43rd International Symposium on Symbolic and Algebraic Computation (ISSAC '18), July 2018, New York (USA). pdf
  2. J. Gómez-Torrecillas, F. J. Lobillo and G. Navarro, Skew Reed-Solomon Codes: Construction and Decoding, in the 5th IEEE Spanish Workshop on Signal Processing, Information Theory and Communications. Barcelona (Spain), January 24th, 2017. pdf
  3. J. Gómez-Torrecillas, F. J. Lobillo and G. Navarro, Constructing and decoding a class of convolutional codes, in the 3rd AICA Industrial Workshop 2106, June 2016, Logroño (Spain). pdf
  4. J. Gómez-Torrecillas, F. J. Lobillo and G. Navarro, Separable algebras and Convolutional Codes, in the 39th International Symposium on Symbolic and Algebraic Computation (ISSAC '14), July 2014, Kobe (Japan). Distinguished Poster Award. pdf
  5. G. Navarro, On path coalgebras of quivers with relations of tame comodule type, in the International Congress of Mathematicians (ICM2006), August 2006, Madrid (Spain). pdf
  6. G. Navarro, Semicentral and split idempotents, in the III Seminario de CategorÌas y Aplicaciones (SECA III), September 2005, Santiago de Compostela (Spain).pdf

Talks

  1. P. Jara, L. Merino, Gabriel Navarro and E. Santos, On lattice orders on hesitant fuzzy sets, XXI Congreso de Tecnologías y Lógica Fuzzy (ESTYLF’22), Toledo, Universidad de Castilla-La Mancha,2022.
  2. M. P. Cuéllar, J. Gómez-Torrecillas, J. Lobillo and G. Navarro, Heuristic methods for computing the distance of linear codes, in the Congreso Bienal de la Real Sociedad Matemática Española, Ciudad Real (Spain), 17-21 January 2022. slides
  3. J. Gómez-Torrecillas, P. Kutas, J. Lobillo and G. Navarro, Decoding constacyclic codes by means of non commutative polynomials, in the Congreso Bienal de la Real Sociedad Matemática Española, Santander (Spain), 4-8 February 2019. slides
  4. J. Gómez-Torrecillas, J. Lobillo and G. Navarro, Computing free distances of idempotent convolutional codes, in the 43th International Symposium on Symbolic and Algebraic Computation (ISSAC 2018), July 2018, New York (USA). slides
  5. J. Gómez-Torrecillas, J. Lobillo and G. Navarro, Skew cyclic codes, in Some Trends in Algebra 2017, September 2017, Prague (Czech Republic). slides
  6. J. Gómez-Torrecillas, J. Lobillo and G. Navarro, Decoding skew RS codes, in IV Encuentro conjunto RSME-SMM 2017, June 2017, Valladolid (Spain). slides
  7. J. Gómez-Torrecillas, J. Lobillo and G. Navarro, Códigos convolucionales cíclicos torcidos, in JNIC2016 (Jornadas Nacionales de Investigación en Ciberseguridad), June 2016, Granada (Spain).
  8. J. Gómez-Torrecillas, J. Lobillo and G. Navarro, Constructing and decoding a class of convolutional codes, in XIII Non-Commutative Algebra days, June 2016, Cádiz (Spain). slides
  9. J. Gómez-Torrecillas, J. Lobillo and G. Navarro, Separable automorphisms on matrix algebras over finite field extensions: applications to ideal codes., in the 40th International Symposium on Symbolic and Algebraic Computation (ISSAC 2015), July 2015, Bath (England). slides
  10. J. Gómez-Torrecillas, J. Lobillo and G. Navarro, Cyclic convolutional codes over separable extensions, in the IV Castle Meeting on Coding Theory and Applications, September 2014, Palmela Castle (Portugal). slides
  11. J. Gómez-Torrecillas, J. Lobillo and G. Navarro, On isomorphisms of modules over non-commutative PDI, in the 39th International Symposium on Symbolic and Algebraic Computation (ISSAC 2014), July 2014, Kobe (Japan). slides
  12. J. Gómez-Torrecillas, J. Lobillo and G. Navarro, A similarity test for Ore polynomials, in the XIV Encuentro de Álgebra Computacional y Aplicaciones (EACA 2014), June 2014, Barcelona (Spain). slides
  13. O. Cortadellas, J. López Peña and G. Navarro, Prime fuzzy ideals over noncommutative rings, in the XIII Encuentro de Álgebra Computacional y Aplicaciones (EACA 2012), June 2012, Alcalá de Henares (Spain). slides
  14. O. Cortadellas, F. J. Lobillo and G. Navarro, Prime fuzzy ideals over noncommutative rings, in XI Jornadas de Teoría de Anillos, May 2012, Granada (Spain). slides
  15. O. Cortadellas, J. López Peña and G. Navarro, Factorization structures with a 2-dimensional factor, in The First International Conference on Mathematics and Statistics, March 2010, Sharjah (United Arab Emirates). slides
  16. O. Cortadellas, J. López Peña and G. Navarro, Quantum duplicates of algebras, in the Journèe d'Algèbre, March 2008, Tetouan (Morocco). slides
  17. J. Gómez-Torrecillas and G. Navarro, Serial coalgebras and their valued Gabriel quivers, in the International Conference on Noncommutative Rings and Geometry, September 2007, Almería (Spain). slides
  18. G. Navarro, Localization in coalgebras and applications to their representation theory, in the XII International Conference on Representation of Algebras (ICRA12), August 2007, Torun (Poland). slides
  19. J. López-Peña and G. Navarro, On the classification and properties of noncommutative duplicates, in the XVI International Colloquium on Integrable Systems and Quantum Symmetries (ISQS-16), June 2007, Prague (Czech Republic). slides
  20. G. Navarro, Simple and injective comodules and localization in coalgebras, in the New techniques in Hopf algebras and graded ring theory international conference, September 2006, Brussels (Belgium). slides
  21. P. Jara, L. Merino, G. Navarro and J. F. Ruíz, On stable localizations of coalgebras, in the Congreso Internacional Mediterraneo de Matemáticas (CIMMA '05), June 2005, Almería (Spain). slides
  22. P. Jara, L. Merino and G. Navarro, Localización y teoría de representación de coálgebras, in the Seminario de Álgebra No Conmutativa, May 2005, Almuñecar (Spain). slides
  23. P. Jara, L. Merino and G. Navarro, Representación de coálgebras, in the VIII Jornadas de Teoría de Anillos, February 2004, Oviedo (Spain). slides

Teaching (25-26)

Álgebra Lineal y Geometría

1º semestre, Grado en Ingeniería de Tecnologías de Telecomunicación
  • Prácticas GITA1: Viernes 11:30--13:30, 1.7
  • Prácticas GITA2: Lunes 11:30--13:30, 1.6
  • Prácticas GITA3: Jueves 11:30--13:30, 1.1
  • Contenidos: Web de PRADO

Lógica y Método Discretos

2º semestre, Grado en Ingeniería Informática
  • Teoría A: Martes (9:30--11:30, 0.2) y Viernes (11:30--12:30, 0.2)
  • Prácticas A1: Lunes (10:30--11:30, 1.3)
  • Prácticas A2: Martes (11:30--12:30, 1.1)
  • Prácticas A3: Jueves (12:30--13:30, 1.4)
  • Contenidos: Web de PRADO

Matemáticas Aplicadas a la Informática (MAI)

1º semestre, Master Universitario en Matemáticas
  • Seminario 1 del IMAG: 8/10, 15/10, 20/10, 22/10, 27/10, 29/10, 5/11, 12/11, 19/11 (16:00 - 18:30)
  • Contenidos: SWAD

Others

  1. Curso de Linux. Introducción al SO Linux

Contact Details

Address: Departamento de Álgebra
Facultad de Ciencias
Universidad de Granada
Calle Fuentenueva s/n
18071, Granada, Spain

Phone: --
Fax: --
E-Mail: gnavarro@ugr.es