Investigación.

    Temas de Interés | Prepublicaciones | Publicaciones | Conferencias Impartidas

Temas de interés:

Actualmente estoy interesado en los siguientes temas:
  • Representaciones de Groupoides y Fibrados Vectoriales: Groupoides Topológicos; Funciones representativas; Bi-Fibrados Principales; Algebroides de Lie y Groupoides de Lie; Álgebras de convolución y Teoremas de reconstrucción.
  • Algebroides de Hopf: Propiedades relacionados con groupoides; Teoremas de estructura; Teoría de Morita; (Co)Homológica y (Co)Homología (Co)Cíclica de categorías de cómodulos.
  • Categorías Pseudo-Tannakianas: Sus detecciones en Álgebra y Geometría; Aplicaciones à la Dualidad de Tannaka-Krein y La Teoría de Galois-Grothendieck.
  • Operadores diferenciales y Espacios Jets: Álgebras de operadores diferenciales; Teoría de Galois diferencial; Anillos de Picard-Vessiot y Algebroides de Hopf Completos.
  • Bicategorías: Categorías monoidales; Bimodulos Invertibles; Monoides de Azumaya; Grupos de Picard; Grupos de Brauer.
  • Álgebra Homológica: Homología y CoHomología; (Co)Homología (Co)Cíclica; Cohomología No Abeliana.

Actas de congreso editadas:

Prepublicaciones:

Publicaciones:

  1. (Con Leonardo Spinosa) On Burnside Theory for groupoids. Bull. Math. Soc. Sci. Math. Roumanie (por aparecer).
  2. (Con Alessandro Ardizzoni y Paolo Saracco) Toward differentiation and integration between Hopf algebroids and Lie algebroids. Publicacions Matemàtiques (2023) Vol. 67, 3--88.
  3. (Con José Gómez-Torrecillas) On the finite dual of a co-commutative Hopf algebroid. Application to linear differential matrix equations and Picard-Vessiot theory. Bulletin of the Belgian Mathematical Society- Simon Stevin (2021) Vol. 28 (1), 53--121.
  4. (Con Paolo Saracco) The Hopf algebroid structure of differentially recursive sequences. Quaestiones Mathematicae (2022) Vol. 45 (4), 547--593.
  5. BOCSES over small linear categories and corings. In: Associative and Non-Associative Algebras and Applications. Springer Proceedings in Mathematics & Statistics, Vol. 311 (2020). M. Siles Molina et al. (eds.), pp. 273--286.
  6. (Con Leonardo Spinosa) Categorified groupoid-sets and their Burnside ring. Turkish Journal of Mathematics (2019) Vol. 43, 2069--2096.
  7. (Con Juan Jesús Barbarán Sánchez) Linear Representations and Frobenius Morphisms of Groupoids. Symmetry, Integrability and Geometry: Methods and Applications (2019) Vol. 15, 019 (33 pp).
  8. (Con Leonardo Spinosa) Mackey formula for bisets over groupoids. Journal of Algebra and Its Applications (2019) Vol. 18, No. 6, 1950109 (35 pp).
  9. (Con Paolo Saracco) Topological tensor product of bimodules, complete Hopf Algebroids and convolution algebras.
    Communications in Contemporary Mathematics (2019) Vol. 21, No.6, 1850015 (53 pp).
  10. (Con Paolo Saracco) Comparing topologies on linearly recursive sequences. ARS Mathematica Contemporanea (2019) Vol. 16, 319--329.
  11. On geometrically transitive Hopf algebroids. Journal of Pure and Applied Algebra (2018) Vol. 222, 3483--3520.
  12. (Con Niels Kowalzig) Morita Theory for Hopf algebroids, principal bibundles and weak equivalences. Documenta Mathematica (2017) Vol. 22, 551-609.
  13. (Con Alessandro Ardizzoni) Invertible Bimodules, Miyashita action and Azumaya Monoids. Nagoya Mathematical Journal (2017) Vol. 225,1--63.
  14. (Con Alessandro Ardizzoni y Paolo Saracco) Functorial constructions for non-associative algebras with applications to quasi-bialgebras. Journal of Algebra (2016) Vol. 449, 460--496.
  15. (Con José Gómez-Torrecillas) Hereditary triangular matrix comonads. Linear Multilinear Algebra (2016) Vol. 64, no. 6, 1032--1055.
  16. (Con Niels Kowalzig) Morita Base Change in Hopf-Cyclic (Co)Homology. Letters in Mathematical Physics (2013) Vol.103, 665--699.
  17. (Con Alessandro Ardizzoni y Claudia Menini) Coendomorphism left bialgebroids. Journal of Algebra and its Applications (2013) Vol.12(03), (21 pages).
  18. (Con Alessandro Ardizzoni y Claudia Menini) Categories of comodules and chain complexes of modules. International Journal of Mathematics (2012), Vol.23(10), (36 pages).
  19. (Con José Gómez-Torrecillas) Invertible unital bimodules over rings with local units, and related exact sequences of groups, II. Journal of Algebra (2012), Vol.370, 266--296.
  20. (Con José Gómez-Torrecillas) On the set of grouplikes of a coring. Acta Mathematica Sinica (English Series) (2012), Vol.28(1), 195--204.
  21. (Con José Gómez-Torrecillas) Coinduction functor and simple comodules. Annali dell'Universitá di Ferrara. Sezione VII. Scienze Matematiche (2010), Vol.56(1), 21--35.
  22. Extended distributive law. Cowreath over corings. Journal of Algebra and its Applications (2010), Vol.9(1), 135--171.
  23. (Con Tomasz Brzeziński y Christian Lomp) Non-commutative integral forms and twisted multi-derivations. Journal of Noncommutative Geometry (2010), Vol.4(2), 289--312.
  24. (Con José Gómez-Torrecillas) Invertible unital bimodules over rings with local units, and related exact sequences of groups. Journal of Algebra (2010), Vol.323(1), 224--240.
  25. Compatibility conditions between rings and corings. Communications in Algebra (2009), Vol.37(5), 1491--1515.
  26. Corings over rings with local units. Mathematische Nachrichten (2009), Vol.282(5), 726--747.
  27. (Con José Gómez-Torrecillas) Corings with decomposition and semiperfect corings. Algebras and Representation Theory (2009), Vol.12(2-5), 343--356.
  28. (Con Joost Vercruysse) Cohomology for bicomodules: separable and Maschke functors. Journal of K-Theory (2009), Vol.3(1), 123--152.
  29. (Con José Gómez-Torrecillas) Corings with exact rational functors and injective objects. In:Modules and comodules, Trends Math., Birkhäuser Verlag, Basel, 2008, pp 185--201.
  30. Wide Morita contexts in bicategories. The Arabian Journal for Science and Engineering. Section C. Theme Issues (2008), Vol.33(2), 153--173.
  31. (Con José Luis Bueso y José Gómez-Torrecillas) Inégalité de Bernstein pour une localisation simple de l'espace symplectique quantique. Communications in Algebra (2006), Vol.34(10), 3615--3627.
  32. (Con Tomasz Brzeziński y José Gómez-Torrecillas) The bicategories of corings. Journal of Pure and Applied Algebra 205 (2006), Vol.205(3), 510--541.
  33. (Con José Gómez-Torrecillas) Comatrix corings and invertible bimodules. Annali dell'Universitá di Ferrara. Sezione VII. Scienze Matematiche (2005), Vol.51, 263--280.
  34. Monoidal categories of corings. Annali dell'Universitá di Ferrara. Sezione VII. Scienze Matematiche (2005), Vol.51, 197--207.
  35. (Con José Gómez-Torrecillas) Morita duality for corings over quasi-Frobenius rings. In: Hopf algebras in noncommutative geometry and physics.
    Lecture Notes in Pure and Appl. Math., 239, Dekker, New York, 2005, pp 137--153.
  36. (Con José Gómez-Torrecillas y Fco. Javier Lobillo) Semisimple corings. Algebra Colloquium (2004), Vol.11, 427--442.
  37. (Con José Gómez-Torrecillas) Infinite comatrix corings. International Mathematics Research Notices (2004), Vol.39, 2017--2037.
  38. (Con José Gómez-Torrecillas) Sur une classe d'extensions de Ore itérées. Bulletin des Sciences Mathématiques (2004), Vol.128(1), 57--76.
  39. (Con José Gómez-Torrecillas) Comatrix corings: Galois corings, descent theory, and a structure theorem for cosemisimple corings. Mathematische Zeitschrift (2003), Vol.244(4), 887--906.
  40. (Con José Gómez-Torrecillas) The group of automorphisms of the coordinate ring of quantum symplectic space. Beiträge zur Algebra und Geometrie (2002), Vol.43(2), 597--601.
  41. (Con L'Moufadal Ben Yakoub y Marie Paule Malliavin) Sur les algèbres d'Heisenberg quantiques. Communications in Algebra (2002), Vol.30(1), 129--148.
  42. (Con José Gómez-Torrecillas) Prime and primitive ideals of a class of iterated skew polynomial rings. Journal of Algebra (2001), Vol.244(1), 186--216.
  43. (Con José Gómez-Torrecillas y L'Moufadal Ben Yakoub) Prime ideals of the coordinate ring of quantum symplectic space. Communications in Algebra (2001), Vol.29(7), 3179--3197.

Conferencias Impartidas: