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Super-cocharacters, star-cocharacters and multiplicities bounded by one

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Abstract

Let A be an algebra over a field of characteristic zero with an additional structure of superalgebra or algebra with involution. The ordinary representation theory of the hyperoctahedral group \({\mathbb{Z}_2\wr S_n}\) is exploited in order to study the super-identities or the star-identities of A. One associates to A a sequence \({\chi_n^{\mathbb{Z}_2}(A), n=1,2,\ldots,}\,{\rm of}\,\mathbb{Z}_2\wr S_n\) -characters and one of the main objective of the theory is to determine their decomposition into irreducibles. Here we classify the super-identities and the star-identities in case the corresponding multiplicities are bounded by one. This is strictly related to the varieties of algebras whose lattice of subvarieties is distributive.

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Authors and Affiliations

  1. Dipartimento di Matematica e Applicazioni, Università di Palermo, Via Archirafi 34, 90123, Palermo, Italy

    A. Giambruno

  2. Department of Algebra and Geometric Computations, Ulyanovsk State University, 432970, Ulyanovsk, Russia

    S. Mishchenko

Authors
  1. A. Giambruno
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  2. S. Mishchenko
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Correspondence to A. Giambruno.

Additional information

A. Giambruno was partially supported by MIUR of Italy. S. Mishchenko was partially supported by RFBR grant 07-01-00080.

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Giambruno, A., Mishchenko, S. Super-cocharacters, star-cocharacters and multiplicities bounded by one. manuscripta math. 128, 483–504 (2009). https://doi.org/10.1007/s00229-008-0243-2

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  • DOI: https://doi.org/10.1007/s00229-008-0243-2

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