Pointed Hopf algebras over finite simple groups

Speaker: Nicolás Andruskiewitsch

Affiliation: Universidad Nacional de Córdoba - CONICET

Abstract

We show that every finite-dimensional pointed Hopf algebra over a finite simple Chevalley group, different from PSL_2(q) with q= 3 mod 4 (and from PSL_3(2)\simeq PSL_2(7)), is isomorphic to the corresponding group algebra.

To do this, we complete the analysis of the Nichols algebras of Yetter-Drinfeld modules over such groups whose support is a semisimple orbit, begun in arXiv:1506.06794, arXiv:2301.03361. In addition to the techniques used in loc. cit., we introduce a general procedure to determine when a semisimple  conjugacy class in a Chevalley or Steinberg group is of type C and a new criterion based on the results of arXiv:2411.02304 that applies to arbitrary racks. 

Throughout the process, we obtain results on Nichols algebras over racks beyond the framework of Chevalley groups.

Bio

Professor Nicolás Andruskiewitsch is a prominent Argentine mathematician, best known for his outstanding contributions to the theory of Hopf algebras and quantum groups. His work has been published in some of the most prestigious mathematical journals. He will be visiting us from 25 May to 10 June through the SMRI International Visitor Program.