Semisimplicity of the deformations of the subcharacter algebra of an\n abelian group

2021/02/25 by İsmail Alperen Öğüt, Öğüt, İsmail Alperen
Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Primary 19A22 #Representation Theory (math.RT) #Secondary 16B50

paper · pdf · doi:10.48550/arxiv.2103.00003

openalex publication_date 2021/02/25 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

For those deformations that satisfy a certain non-degeneracy condition, we\ndescribe the structure of certain simple modules of the deformations of the\nsubcharacter algebra of a finite group. For finite abelian groups, we prove\nthat the deformation given by the inclusion of the natural numbers, which\ncorresponds to the algebra generated by the fibred bisets over a field of\ncharacteristic zero, is not semisimple. In the cyclic group of prime order\ncase, we provide a complete description of the semisimple deformations.\n

Related

• Semisimplicity of some deformations of the subgroup category and the biset category
• Semicharacters of Groups
• Simple Hopf algebras and deformations of finite groups
• The generalisation of some invariants of modules to groups with\n operators
• Some deformations of the fibred biset category