GABRIEL NAVARRO

Department of Computer Sciences and AI
University of Granada

About me

At present, I have a permanent position (Profesor Titular de Universidad) at the Department of Computer Sciences and Artificial Intelligence of the University of Granada.


Research Interests

Ring Theory
Representation Theory of Algebras
Non-commutative Localization
Non-commutative Geometry
Fuzzy/Rough/Soft Sets Theory
Symbolic Computation
Coding Theory

Publications

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

  1. J. Gómez-Torrecillas, E. Hieta-Aho, F. J. Lobillo, S. López-Permouth, G. Navarro, Some remarks on non projective Frobenius algebras and linear codes, Designs, Codes and Cryptography 2019. 10.1007/s10623-019-00666-1
  2. J. Gómez-Torrecillas, F. J. Lobillo and Gabriel Navarro, Cyclic Distances of Idempotent Convolutional Codes, Journal of Symbolic Computation 2019. 10.1016/j.jsc.2019.10.008
  3. J. Gómez-Torrecillas, F.J. Lobillo and G. 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
  4. J. Gómez-Torrecillas, F.J. Lobillo, and G. 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
  5. J. Gómez-Torrecillas, F.J. Lobillo and G. 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
  6. F.J. Lobillo, L. Merino, G. 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
  7. J. Gómez-Torrecillas, F.J. Lobillo and G. 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
  8. J. Gómez-Torrecillas, F.J. Lobillo, G. 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
  9. J. Gómez-Torrecillas, F.J. Lobillo, and G. Navarro, Peterson-Gorenstein-Zierler algorithm for skew RS codes, Linear and Multilinear Algebra 66 (2018), 469-487. 10.1080/03081087.2017.1301364
  10. J. Gómez-Torrecillas, F.J. Lobillo, and G. Navarro, A Sugiyama-like decoding algorithm for convolutional codes, IEEE Transactions on Information Theory 63 (2017) 6216-6226.10.1109/TIT.2017.2682856
  11. J. Gómez-Torrecillas, F.J. Lobillo, and G. Navarro, Ideal codes over separable ring extensions, IEEE Transactions on Information Theory 65 (2017), 2796-2813. 10.1109/TIT.2017.2682856
  12. J. Gómez-Torrecillas, F.J. Lobillo, and G. Navarro, Computing separability elements for the sentence–ambient algebra of split ideal codes, Journal of Symbolic Computation 83 (2017), 211-227. 10.1016/j.jsc.2016.11.012
  13. J. Gómez-Torrecillas, F.J. Lobillo, and G. Navarro, A new perspective of cyclicity in convolutional codes, IEEE Transactions on Information Theory 62 (5) (2016), 2702-2706. 10.1109/TIT.2016.2538264
  14. F.J. Lobillo, L. Merino, G. Navarro and E. Santos, Rough ideals under relations associated to fuzzy ideals, Information Sciences 352-353 (2016), 121-132. 10.1016/j.ins.2016.02.058
  15. J. Gómez-Torrecillas, F. J. Lobillo and G. 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
  16. J. Gómez-Torrecillas, F. J. Lobillo and G. Navarro, Convolutional codes with a matrix-algebra word-ambient, Advances in Mathematics of Communication 10 (2016), 29-43. 10.3934/amc.2016.10.29
  17. J. Gómez-Torrecillas, F.J. Lobillo and G. 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
  18. J. Gómez-Torrecillas, F. J. Lobillo and G. 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
  19. 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
  20. J. Gómez-Torrecillas, F.J. Lobillo, and G. 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
  21. J. Gómez-Torrecillas, F. J. Lobillo and G. Navarro, Generating idempotents in ideal codes, ACM Communications in Computer Algebra 48 (3/4) (2014), 113-115. 10.1145/2733693.2733703
  22. J. Gómez-Torrecillas, F.J. Lobillo and G. Navarro, On isomorphisms of modules over non-commutative PID, 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
  23. J. Gómez-Torrecillas, F.J. Lobillo and G. 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
  24. G. 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
  25. G. 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
  26. P. Jara, J. López Peña, G. 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
  27. O. Cortadellas, J. López Peña and G. Navarro, Factorization structures with a 2-dimensional factor, J. London Math. Soc 81 (2010), 1-23. 10.1112/jlms/jdp055
  28. P. Jara, L. Merino, G. Navarro and J.F. Ruíz, Prime path coalgebras, Arab. J. Sci. Eng. 33 (2008), Number 2C, 273-283. arxiv link
  29. J. Gómez-Torrecillas and G. Navarro, Serial coalgebras and their valued Gabriel quivers, J. Algebra 319 (2008), 5039-5059. 10.1016/j.jalgebra.2008.03.020
  30. J. López Peña and G. Navarro, On the classification and properties of noncommutative duplicates, K-Theory 38 (2008), 223-234. 10.1007/s10977-007-9017-y
  31. G. Navarro, Some remarks on localization in coalgebras, Comm. Algebra 36 (2008), 3447-3466. 10.1080/00927870802107868
  32. R. M. Ibañez Cobos, J. López Peña and G. Navarro, A note on generalized path algebras, Rev. Roumaine Math. Pures Appl. 53(1) (2008), 25-36. Rrc8_1
  33. G. Navarro, Simple comodules and localization in coalgebras, in: Contactforum New techniques in Hopf algebras and graded ring theory, KVAB 2007, 145-164.
  34. P. Jara, L. M. Merino and G. Navarro, Localization in tame and wild coalgebras, J. Pure Appl. Algebra 211 (2007), 342-359. 10.1016/j.jpaa.2007.01.009
  35. P. Jara, L. M. Merino, G. Navarro and F. Ruiz, Localization in coalgebras. Stable localizations and path coalgebras, Comm. Algebra 34 (2006), 2843-2856. 10.1080/00927870802107868
  36. P. Jara, L. M. Merino and G. 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 J. P. Sánchez-Hernández, Peterson-Gorenstein-Zierler algorithm for differential convolutional codes, 2019.
  2. J. Gómez-Torrecillas, P. Kutas, F. J. Lobillo and Gabriel Navarro, Primitive idempotents in central simple algebras over $\mathbb{F}_q(t)$ with an application to coding theory, 2019.
  3. F.J. Lobillo, L. Merino, G. Navarro and E. Santos, Induced triangular norms and negations on bounded lattices, 2019.
  4. J. Gómez-Torrecillas, F. J. Lobillo, Gabriel Navarro and J. P. Sánchez-Hernández, Biseparable extensions are not necessarily Frobenius, 2019.

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. 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
  2. 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
  3. J. Gómez-Torrecillas, J. Lobillo and G. Navarro, Skew cyclic codes, in Some Trends in Algebra 2017, September 2017, Prague (Czech Republic). slides
  4. J. Gómez-Torrecillas, J. Lobillo and G. Navarro, Decoding skew RS codes, in IV Encuentro conjunto RSME-SMM 2017, June 2017, Valladolid (Spain). slides
  5. J. Gómez-Torrecillas, J. Lobillo and G. Navarro, Códigos convolucionales cíclicos torcidos, in JNIC2016 (Jornadas Nacionales de Investigación en Ciberseguridad), June 2016, Granada (Spain).
  6. 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
  7. 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
  8. 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
  9. 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
  10. 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
  11. 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
  12. 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
  13. 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
  14. O. Cortadellas, J. López Peña and G. Navarro, Quantum duplicates of algebras, in the Journèe d'Algèbre, March 2008, Tetouan (Morocco). slides
  15. 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
  16. 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
  17. 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
  18. 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
  19. P. Jara, L. Merino and G. Navarro, Localization and comodule types of coalgebras, in the Algebras and Coalgebras Conferences: Tools for Geometry, Physics and Computer Science, March 2006, Cairo (Egypt). slides
  20. 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
  21. 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
  22. P. Jara, L. Merino and G. Navarro, Representación de coálgebras, in the VIII Jornadas de Teoría de Anillos, February 2004, Oviedo (Spain). slides

Teaching (19-20)

Fundamentos de Programación

  • 1º semestre, Doble Grado Informática/Matemáticas
  • Teoría: Miércoles 18:30--19:30, Jueves 18:30--19:30, 1.8
  • Prácticas 1: Miércoles 15:30--17:30, 2.1
  • Prácticas 2: Jueves 15:30--17:30, 2.8
  • Contenidos: Web de PRADO

Modelos Avanzados de Computación

  • 6º semestre, Grado en Ingeniería Informática
    (Computación y Sistemas Inteligentes)
  • Prácticas MCA1: Martes (17:30--19:30, 3.2)
  • Prácticas MCA2: Miércoles (17:30--19:30, 3.2)
  • Contenidos: Web de PRADO

Modelos de Computación

  • 5º semestre, Doble Grado Informática/Matemáticas
  • Prácticas MC1: Jueves (19:30--21:30, 3.2)
  • Contenidos: Web de PRADO

Modelos de Computación

  • 5º semestre, Grado en Ingeniería Informática
  • Prácticas A3: Martes (17:30--19:30, 3.2)
  • Contenidos: Web de PRADO

Others

  1. Curso de Linux. Introducción al SO Linux

Contact Details

Address: Escuela Técnica Superior de Ingenierías Informática y de Telecomunicaciones.
                    C/ Periodista Daniel Saucedo Aranda, s/n
                    18071, Granada, España.

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