Variants on a conjecture relating block source algebras to\n characteristic bisets

2019/09/04 by Laurence Barker, Barker, Laurence, Matthew Gelvin +1
Engineering · Materials Science · Mathematics · #20C20 #20D20 #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Representation Theory (math.RT) #Synthesis and properties of polymers #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1909.01834

openalex publication_date 2019/09/04 · openalex created_date 2022/09/14 · openalex updated_date 2026/07/28

Abstract

Given a block of a finite group, any source algebra has a basis invariant\nunder the multiplicative actions of the defect group. Is such a basis a\ncharacteristic biset of the block fusion system? If the basis can be chosen to\nconsist entirely of units, the question is answered in the affirmative. We\nprove the equivalence of several reformulations of this stronger condition on\nthe source algebra.\n

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