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


Author: V. A. Artamonov
Translated by: N. A. Vavilov
Original publication: Algebra i Analiz, tom 26 (2014), nomer 2.
Journal: St. Petersburg Math. J. 26 (2015), 207-223
MSC (2010): Primary 16T05
DOI: https://doi.org/10.1090/S1061-0022-2015-01337-X
Published electronically: February 3, 2015
MathSciNet review: 3242035
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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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Additional Information

V. A. Artamonov
Affiliation: Department of Mechanics and Mathematics, Moscow State University, Vorobievy Gory 1, 119991 Moscow, Russia
Email: artamon@mech.math.msu.su

DOI: https://doi.org/10.1090/S1061-0022-2015-01337-X
Keywords: Hopf algebras, projective representations
Received by editor(s): August 14, 2013
Published electronically: February 3, 2015
Additional Notes: Supported by RFBR (grant no. 12-01-00070)
Article copyright: © Copyright 2015 American Mathematical Society