Hopf Subalgebras and Hopf Ideals of Certain Semisimple Hopf Algebras

R. B. Mukhatov

M. V. Lomonosov Moscow State University

Abstract: In the paper, for semisimple Hopf algebras that have only one non-one-dimensional irreducible representation, all Hopf ideals are described and, under some restriction concerning the number of group elements in the dual Hopf algebra, some series of Hopf subalgebras are found. Moreover, the quotient Hopf algebras of these semisimple Hopf algebras are described.

Keywords: Hopf algebra, dual Hopf algebra, irreducible representation, semisimple decomposition, quotient Hopf algebra, projective representation.

UDC: 512.667

Received: 03.10.2010
Revised: 24.08.2011

DOI: 10.4213/mzm9040

 English version: Mathematical Notes, 2013, 93:1, 143–150

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