This article is cited in 3 papers

On Finite-Dimensional Semisimple Hopf Algebras of Dimension $n(n+1)$

S. Yu. Spiridonova

M. V. Lomonosov Moscow State University

Abstract: We study finite-dimensional semisimple Hopf algebras over an algebraically closed field which have only one summand of dimension greater than $1$ in their semisimple decompositions and assume that the group of group elements in the dual Hopf algebra is cyclic and has minimal order. Under given constraints, we obtain a detailed description of the comultiplication and the antipode.

Keywords: semisimple Hopf algebra, comultiplication, antipode, coassociativity of comultiplication, semisimple decomposition, homomorphism, cocommutative Hopf algebra.

UDC: 512.667.7

Received: 12.05.2010

DOI: 10.4213/mzm9308

 English version: Mathematical Notes, 2012, 91:2, 243–258

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