KERNELS OF REPRESENTATIONS AND COIDEAL SUBALGEBRAS OF HOPF ALGEBRAS

Abstract

AbstractWe 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 Andruskiewitsch and Devoto [Extensions of Hopf algebras, Algebra i Analiz7 (1995), 22–69]. Brauer's theorem for kernels over group algebras is generalised to Hopf algebras.