Miriam Cohen and Sara Westreich: Hit-invariants and commutators for Hopf algebras, p.299-313

Abstract:

We continue studying normal left coideal subalgebras of a Hopf algebra $H,$ realizing them as invariants of $H$ under the left hit action of Hopf subalgebras of $H^*.$ We apply this realization to test an equivalence relation on irreducible characters for two important examples. The commutator sublagebra of $H,$ which is the analogue of the commutator subgroup of a group and the image of the Drinfeld map for quasitriangular Hopf algebras. We end with the example $H = D(kS_3)$ where commutators are computed.

Key Words: Normal left coideal subalgebras, left kernels, commutators, commu- tator algebra, Drinfeld map.

2010 Mathematics Subject Classification: Primary: 16T05;

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