Research.

Publicaciones:

1. (With Leonardo Spinosa) On Burnside Theory for groupoids. Bull. Math. Soc. Sci. Math. Roumanie (to appear).
2. (With Alessandro Ardizzoni and Paolo Saracco) Towards differentiation and integration between Hopf algebroids and Lie algebroids. Publicacions Matemàtiques (to appear).
3. (With 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. (With 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. (With Leonardo Spinosa) Categorified groupoid-sets and their Burnside ring. Turkish Journal of Mathematics (2019) Vol. 43, 2069--2096.
7. (With 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. (With Leonardo Spinosa) Mackey formula for bisets over groupoids. Journal of Algebra and Its Applications (2019) Vol. 18, No. 6, 1950109 (35 pp).
9. (With 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. (With 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. (With Niels Kowalzig) Morita Theory for Hopf algebroids, principal bibundles and weak equivalences. Documenta Mathematica (2017) Vol. 22, 551--609.
13. (With Alessandro Ardizzoni) Invertible Bimodules, Miyashita action and Azumaya Monoids. Nagoya Mathematical Journal (2017) Vol. 225, 1--63.
14. (With Alessandro Ardizzoni and Paolo Saracco) Functorial constructions for non-associative algebras with applications to quasi-bialgebras. Journal of Algebra (2016) Vol. 449, 460--496.
15. (With José Gómez-Torrecillas) Hereditary triangular matrix comonads. Linear Multilinear Algebra (2016) Vol. 64, no. 6, 1032--1055.
16. (With Niels Kowalzig) Morita Base Change in Hopf-Cyclic (Co)Homology. Letters in Mathematical Physics (2013) Vol.103, 665--699.
17. (With Alessandro Ardizzoni and Claudia Menini) Coendomorphism left bialgebroids. Journal of Algebra and its Applications (2013) Vol.12(03), (21 pages).
18. (With Alessandro Ardizzoni and Claudia Menini) Categories of comodules and chain complexes of modules. International Journal of Mathematics (2012), Vol.23(10), (36 pages).
19. (With 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. (With José Gómez-Torrecillas) On the set of grouplikes of a coring. Acta Mathematica Sinica (English Series) (2012), Vol.28(1), 195--204.
21. (With 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. (With Tomasz Brzeziński and Christian Lomp) Non-commutative integral forms and twisted multi-derivations. Journal of Noncommutative Geometry (2010), Vol.4(2), 289--312.
24. (With 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. (With José Gómez-Torrecillas) Corings with decomposition and semiperfect corings. Algebras and Representation Theory (2009), Vol.12(2-5), 343--356.
28. (With Joost Vercruysse) Cohomology for bicomodules: separable and Maschke functors. Journal of K-Theory (2009), Vol.3(1), 123--152.
29. (With 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. (With José Luis Bueso and 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. (With Tomasz Brzeziński and José Gómez-Torrecillas) The bicategories of corings. Journal of Pure and Applied Algebra 205 (2006), Vol.205(3), 510--541.
33. (With 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. (With 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. (With José Gómez-Torrecillas and Fco. Javier Lobillo) Semisimple corings. Algebra Colloquium (2004), Vol.11, 427--442.
37. (With José Gómez-Torrecillas) Infinite comatrix corings. International Mathematics Research Notices (2004), Vol.39, 2017--2037.
38. (With José Gómez-Torrecillas) Sur une classe d'extensions de Ore itérées. Bulletin des Sciences Mathématiques (2004), Vol.128(1), 57--76.
39. (With 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. (With 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. (With L'Moufadal Ben Yakoub and Marie Paule Malliavin) Sur les algèbres d'Heisenberg quantiques. Communications in Algebra (2002), Vol.30(1), 129--148.
42. (With 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. (With José Gómez-Torrecillas and L'Moufadal Ben Yakoub) Prime ideals of the coordinate ring of quantum symplectic space. Communications in Algebra (2001), Vol.29(7), 3179--3197.

Talks in Conferences:

• Conference: Abstract Aspects of Higher Representation Theory.
  Title of the talk: " Picard-Vessiot extensions, differential Galois groupoids and Hopf algebroids".
  Dates: 20-25 January 2019.
  Institute and Country: Université Libre de Bruxelles. Brussels, Belgium.
• Conference: First Morocan Congress On Mathematics and its Applications.
  Titre de l'exposé: "Basic theory of abstract groupoids and their linear representations. Applications".
  Dates: 17-19 December 2018.
  Institute and Country: Université Abdelmalek Essaadi. Faculté Des Sciences de Tetuán. Tetuán, Marocco.
• Conference: The 3rd Moroccan Andalusian meeting on Algebras and their Applications
  Titre de l'exposé: On Groupoids and Hopf Algebroids.
  Dates: 12-14 April 2018.
  Centre et pays: Université Abdelmalek Essaadi. Faculté Des Sciences de Tetuán. Tetuán, Marocco.
• Conference: Bruaer Groups, Hopf Algebras and Monoidal Categories.
  Title of the talk: "Finite dimensional representations of abstract groupoids, representative functions and commutative Hopf algebroids".
  Dates: 24-27 May 2016.
  Institute and Country: Università Degli Studi Di Torino. Torino, Italy.
• Conference: Workshop on Hopf Algebra and Related Topics.
  Title of the talk: Finite dimensional representations of abstract groupoids, representative functions and commutative Hopf algebroids
  Dates: 21-22 January 2016.
  Institute and Country: Università Degli Studi Di Torino. Torino, Italy.
• Conference: Ferrara Algebra Workshop.
  Title of the talk: "Transitive groupoids, principal bisets and weak equivalences".
  Dates: 17-18 Septembre 2015.
  Institute and Country: Università Degli Studi Di Ferrara. Ferrara, Italy.
• Conference: New Trendes in Hopf algebras and Tensor Categories.
  Title of the talk: "New Characterizations of geometraiclly transitive Hopf algebroids".
  Dates: 01-06 June 2015.
  Institute and Country: The Royal Academies for Science and the Arts of Belgium. Brussels, Belgium.
• Conférence: Conferencia de la Real Sociedad Matemática Española. Sesion: Métodos categóricos en álgebra no conmutativa.
  Title of the talk: "Morita Theory for Commutative Hopf Algebroids, and Hovey-Strickland conjecture".
  Dates: 02-06 February 2015.
  Institute and Country: Universidad de Granada. Granada, Spain.
• Conference: International Workshop on Algebra and Applications.
  Title of the talk: Representative functions on discrete groupoids and duality with Hopf algebroids
  Dates: 18-22 June 2014.
  Institute and Country: Université Sidi Mohamed Ben Abdellah Fez. Fez, Marocco.
• Conference: Congreso de la Real Sociedad Matemática Española. Sesion: Teoría de anillos no conmutativos.
  Title of the talk: "Morita invariance in Hopf-cyclic co-homologies".
  Dates: 21-25 January 2013.
  Institute and Country: Universidad de Santiago. Santiago de Compostela, Spain.
• Conference: Interfaces of Noncommutative Geometry with the Representation Theory of Hopf Algebras and Artin Algebras.
  Title of the talk: "The algebraic groupoid structure of the universal Picard-Vessiot ring, differential operators and Jet spaces.".
  Dates: 11-16 August 2012.
  Institute and Country: Istanbul Center of Mathematical Sciences. Istanbul, Turkey.
• Conférence: Algebraic and homological aspects of non commutative geometry.
  Title of the talk: "Categories of comodules and chains complexes of modules".
  Dates: 12-15 Jully 2011.
  Institute and Country: Istanbul Center of Mathematical Sciences. Istanbul, Turkey.
• Conference: International Conference Algebra Geometry Mathematical Physics.
  Title of the talk: "Morita invariance in Hopf-cyclic co-homologies."
  Dates: 24-26 October 2011.
  Institute and Country: Faculté des Sciences et Techniques. University of Haute Alsace. France.
• Conference: International Conference on Mathematics and Statistics. Algebra Session.
  Title of the talk: "Coinduction functors and Simple comodules".
  Dates: 18-21 March 2010.
  Institute and Country: American Universty of Sharja. Sharja, UAE.
• Conference: Rings and Modules.
  Title of the talk: "Invertible unital Bimodules over rings with local units and related exact sequences of groups."
  Dates: 16-19 September 2008.
  Institute and Country: Universidade De Lisboa. Lisbon, Portugal.
• Conference: Noncommutative Structures in Mathematics and Physics.
  Title of the talk: "Galois corings with grouplike elements and related exact sequences".
  Dates: 22-26 July 2008.
  Institute and Country: Vrije Universiteit Brussel. Brussels, Belgium.
• Conference: Workshop on Categorical Groups.
  Title of the talk: "Coendomorphism bialgebroids".
  Dates: 16-20 June 2008.
  Institute and Country: Institut De Matemàtica, Universitat de Barcelona. Barcelona, Spain.
• Conference: Algebra, Representations and Applications.
  Title of the talk: Double Distributive law, rings and corings.
  Dates: 26 August -01 September 2007.
  Institute and Country: Universidade De São Paulo. São Paulo, Brazil.
• Conference: International Conference on Module and comodules.
  Title of the talk: "Corings over rings with local units".
  Dates: 08-10 September 2006.
  Institute and Country: Universidade De Oporto. Oporto, Portugal.
• Conference: New technique in Hopf algebras and graded rings.
  Title of the talk: "Cohomology for bicomodules. Separable and Maschke functors".
  Dates: 18-23 September 2006.
  Institute and Country: Vrije Universiteit Brussel. Brussels, Belgium.
• Conference: International Mediteranean congress of Mathematics.
  Title of the talk: ''Comatrix corings and invertible bimodules''.
  Dates: 06-10 June 2005.
  Institute and Country: Universidad de Almería. Alemría, Spain.
• Conference: Primer Congreso Conjunto de Matemáticas REME-SCM-SEIO-SEMA, Mat.es.2005
      (Sesión de álgebra No conmutativa).
  Title of the talk: ''Coanillos semiperfectos y coanillos con funtor racional exacto''.
  Dates: 01-04 February 2005.
  Institute and Country: Universidad de Valencia. Valencia, Spain.
• Conference: Internacional Workshop Groups, Algebra and Geometries.
  Title of the talk: ''Corings and cotriples''.
  Dates: 23-29 August 2004.
  Institute and Country: Vrije Universiteit Brussel. Brussels, Belgium.
• Conference: Workshop on Hopf algebra.
  Title of the talk: "Finite comatrix corings for corings and bimodules".
  Dates: Swansea, 24-26 June 2004.
  Institute and Country: University of Wales Swansea. Swansea, UK.