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KERNELS OF REPRESENTATIONS AND COIDEAL SUBALGEBRAS OF HOPF ALGEBRAS
SEBASTIAN BURCIU
Journal:

Glasgow Mathematical Journal / Volume 54 / Issue 1 / January 2012

Published online by Cambridge University Press:

02 August 2011, pp. 107-119

Print publication:

January 2012
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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 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.