TY - JOUR

T1 - Character tables and normal left coideal subalgebras

AU - Cohen, Miriam

AU - Westreich, Sara

N1 - Funding Information:
This research was supported by the ISRAEL SCIENCE FOUNDATION , 170-12 .

PY - 2014/10

Y1 - 2014/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84899486783&partnerID=8YFLogxK

U2 - 10.1016/j.jpaa.2014.02.010

DO - 10.1016/j.jpaa.2014.02.010

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AN - SCOPUS:84899486783

SN - 0022-4049

VL - 218

SP - 1845

EP - 1866

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 10

ER -