Character tables and normal left coideal subalgebras

Miriam Cohen, Sara Westreich

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We continue studying properties of semisimple Hopf algebras H over algebraically closed fields of characteristic 0 resulting from their generalized character tables. We show that the generalized character table of H reflects normal left coideal subalgebras of H. These are the Hopf analogues of normal subgroups in the sense that they arise from Hopf quotients. We apply these ideas to prove Hopf analogues of known results in group theory. Among the rest we prove that columns of the character table are orthogonal and that all entries are algebraic integers. We analyze 'semi-kernels' and their relations to the character table. We prove a full analogue of the Burnside-Brauer theorem for almost cocommutative H. We also prove the Hopf algebras analogue of the following (Burnside) theorem: If G is a non-abelian simple group then {1} is the only conjugacy class of G which has prime power order.

Original languageEnglish
Pages (from-to)1845-1866
Number of pages22
JournalJournal of Pure and Applied Algebra
Volume218
Issue number10
DOIs
StatePublished - 1 Jan 2014

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