Hopf algebra representations and tensor categories

Coordinator: Sebastian Burciu

Thursday, May 15, 2014
2:00 pm in Room 309-310 "Gheorghe Vranceanu", IMAR

Adriana Balan (UPB)
An introduction to Hopf monads, (III)

Thursday, January 30, 2014
2:00 pm in Room 309-310 "Gheorghe Vranceanu", IMAR

Adriana Balan (UPB)
An introduction to Hopf monads, (II)

Thursday, January 23, 2014
2:00 pm in Room 309-310 "Gheorghe Vranceanu", IMAR

Adriana Balan (UPB)
An introduction to Hopf monads

Abstract: This is an introduction in the theory of Hopf monads in autonomous categories. We follow the recent developments obtained by Bruguieres, Lack and Virelizier. Hopf monads generalize Hopf algebras to non-braided settings and any monoidal adjunction between autonomous categories gives rise to a Hopf monad. We present extensions of many fundamental results of the theory of Hopf algebras (such as the decomposition of Hopf modules, the existence of integrals, Maschke criterium of semisimplicity etc) to Hopf monads.

Thursday, January 16, 2014
2:00 pm in Room 309-310 "Gheorghe Vranceanu", IMAR

Costel Bontea (Univ. New Hampshire)
Modified supergroup algebras and the classification of finite dimensional triangular Hopf algebras

Abstract: We describe the role of modified supergroup algebras in the classification of finite dimensional triangular Hopf algebras. The talk is based on the papers of N. Andruskiewitsch, P. Etingof and S. Gelaki, "Triangular Hopf algebras with the Chevalley property" (Michigan Math. J. 49, 2001) and of P. Etingof and S. Gelaki, "The classification of finite dimensional triangular Hopf algebras over an algebraically closed field" (Mosc. Math. J. 3, 2003).

Thursday, December 5, 2013
2:00 pm in Room 309-310 "Gheorghe Vranceanu", IMAR

Sebastian Burciu (IMAR)
Class equation and factorizable Hopf algebras, (III)

Thursday, November 28, 2013
2:00 pm in Room 309-310 "Gheorghe Vranceanu", IMAR

Sebastian Burciu (IMAR)
Class equation and factorizable Hopf algebras, (II)

Thursday, November 14, 2013
2:00 pm in Room 309-310 "Gheorghe Vranceanu", IMAR

Sebastian Burciu (IMAR)
Class equation and factorizable Hopf algebras

Abstract: In this talk we present Lorenz's proof for the class equation of a semisimple Hopf algebras. We recall the notion of a factorizable Hopf algebra and we will prove that the Drinfeld double of a Hopf algebra is alawys factorizable. Using class equation we show that the dimension of any irreducible module of a semisimple factorizable Hopf algebra divides the dimension of the Hopf algebra.

Thursday, November 7, 2013
2:00 pm in Room 309-310 "Gheorghe Vranceanu", IMAR

Sebastian Burciu (IMAR)
Character theory for semisimple Hopf algebras

Abstract: The character algebra of an arbitrary Hopf algebra is defined. In analogy to group representation theory we prove some properties of the character algebra for finite dimensional Hopf algebras. For a semisimple Hopf algebra we show that the character algebra is also semisimple and that the orthogonality relations hold.