La jornada constará de dos seminarios, con el siguiente cronograma:
* 14.00-15.00: Seminario de Ruben Henrard,
* 15.00-15.30: Café en la Sala de Matemática,
* 15.30-16.30: Seminario de Timmy Fieremans.
Más información sobre cada charla a continuación.
11/04/2017, 14:00 hs, aula 27 FaMAF
Monoidal reconstruction and deformation theory
Expositor: Ruben Henrard (Bélgica)
Resumen: Recently the Green rings of a large class of monoidal categories have been determined. Conversely, the question of which rings appear as the Green ring of monoidal categories received some attention. The aim of this talk is to reconstruct monoidal categories from certain invariants (the Green ring being one of them). Keeping the Green ring fixed and letting the other invariants vary, we obtain all deformations of the tensor category.
11/04/2017, 15:30 hs, aula 27 FaMAF
An introduction to Hopf categories and Galois theory for Hopf categories
Expositor: Timmy Fieremans (Bélgica)
Resumen: Hopf categories enriched over braided monoidal categories were introduced in [1]. The notion is linked to several recently developed notions in Hopf algebra theory, such as Hopf group (co)algebras, weak Hopf algebras and duoidal categories. A short summary of these results will be given.
In [2] Descent theory for linear categories is developed. Given a linear category as an extension of a diagonal category, we introduce descent data, and the category of descent data is isomorphic to the category of representations of the diagonal category, if some flatness assumptions are satisfied. Then Hopf-Galois descent theory for linear Hopf categories, the Hopf algebra
version of a linear category, is developed. This leads to the notion of Hopf-Galois category extension. We will briefly give some important theorems and explain the similarity with the classical results. This is all based on joint work with Stefaan Caenepeel.
[1] E. Batista, S. Caenepeel, J. Vercruysse, “Hopf categories”, Algebras Repres. Theory
19 (2016), 1173-1216.
[2] S. Caenepeel, T. Fieremans, “Descent and Galois theory for Hopf categories”, online
available at arXiv: 1702.01337