Semi-simple Hopf algebras with restrictions on irreducible modules of dimension exceeding 1

Artamonov, V.

doi:10.1090/S1061-0022-2015-01337-X

Semi-simple Hopf algebras with restrictions on irreducible modules of dimension exceeding $1$
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by V. A. Artamonov
Translated by: N. A. Vavilov

St. Petersburg Math. J. 26 (2015), 207-223

DOI: https://doi.org/10.1090/S1061-0022-2015-01337-X

Published electronically: February 3, 2015

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Abstract:

The semisimple finite-dimensional Hopf algebras are considered all of whose irreducible representations of each dimension exceeding $1$ are isomorphic. The Hopf algebras with a unique irreducible representation of dimension exceeding $1$ are described, provided this dimension is equal to the order of the group of group-like elements of the dual Hopf algebra. Under some additional restrictions, it is shown that a Hopf algebra cannot have two irreducible representations of dimension exceeding $1$.

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