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KERNELS OF REPRESENTATIONS AND COIDEAL SUBALGEBRAS OF HOPF ALGEBRAS

Published online by Cambridge University Press:  02 August 2011

SEBASTIAN BURCIU
SEBASTIAN BURCIU*
Affiliation:
Faculty of Mathematics and Computer Science, University of Bucharest, 14 Academiei Street, Bucharest, Romania and Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, Bucharest, 014700, Romania e-mail: [email protected]
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Abstract

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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.

Keywords

MSC 16W30
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 54 , Issue 1 , January 2012 , pp. 107 - 119
Copyright
Copyright © Glasgow Mathematical Journal Trust 2011

References

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