Kernels of representations and coideal subalgebras of Hopf algebras

Details Kernels of representations and coideal subalgebras of Hopf algebras Kernels of representations and coideal subalgebras of Hopf algebras

2010-12-14

arxiv.org/abs/1012.3096v1

Glasgow Math. J. , 54 (1), 2012

Mathematics

Quantum Algebra

16 pages, submitted

Scientific paper

10.1017/S0017089511000395

We define left and right kernels of representations of Hopf algebras. In the case of group algebras, left and right kernels coincide and they are the usual kernels of modules. In the general case we show that these kernels coincide with the categorical left and right Hopf kernels of morphisms of Hopf algebras defined in \cite{AD}. Brauer's theorem for kernels over group algebras is generalized to Hopf algebras.

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