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

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Öğüt İ. A.

Algebras and Representation Theory, cilt.26, sa.2, ss.471-490, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 26 Sayı: 2
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1007/s10468-021-10100-7
  • Dergi Adı: Algebras and Representation Theory
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.471-490
  • Anahtar Kelimeler: Subcharacter algebra, Semisimple category, Semisimple deformation, Fibred biset category, Algebraic independence, BURNSIDE, RING
  • Ankara Üniversitesi Adresli: Evet

Özet

© 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.