Semisimplicity of the Deformations of the Subcharacter Algebra of an Abelian Group


Creative Commons License

Öğüt İ. A.

Algebras and Representation Theory, vol.26, no.2, pp.471-490, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 26 Issue: 2
  • Publication Date: 2023
  • Doi Number: 10.1007/s10468-021-10100-7
  • Journal Name: Algebras and Representation Theory
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, MathSciNet, zbMATH
  • Page Numbers: pp.471-490
  • Keywords: Subcharacter algebra, Semisimple category, Semisimple deformation, Fibred biset category, Algebraic independence, BURNSIDE, RING
  • Ankara University Affiliated: Yes

Abstract

© 2021, The Author(s), under exclusive licence to Springer Nature B.V.For those deformations that satisfy a certain non-degeneracy condition, we describe the structure of certain simple modules of the deformations of the subcharacter algebra of a finite group. For finite abelian groups, we prove that the deformation given by the inclusion of the natural numbers, which corresponds to the algebra generated by the fibred bisets over a field of characteristic zero, is not semisimple. In the cyclic group of prime order case, we provide a complete description of the semisimple deformations.