2017/12/07 by Justin Lynd, Lynd, Justin, Jason Semeraro +1 · 1 citation
Mathematics · #20C20 #20C33 #20D06 #20D20 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebra over a field #Algebraic structures and combinatorial models #Automorphism #Block (permutation group theory) #Combinatorics #Conjugacy class #Discrete mathematics #FOS: Mathematics #Field (mathematics) #Generalization #Group (periodic table) #Group Theory (math.GR) #Listing (finance) #Mathematical analysis #Mathematics #Physics #Pure mathematics #Representation Theory (math.RT) #math.GR #math.RT #msc:20C20 #msc:20C33 #msc:20D06 #msc:20D20
paper · pdf · doi:10.48550/arxiv.1712.02826
published in arXiv (Cornell University) (Cornell University) · v2,3: Major revision including some changes to notation, Section 4 entirely rewritten, many proofs expanded, other improvements. 33 pages, 6 tables, 2 figures
openalex publication_date 2017/12/07 · arxiv created 2019/06/23 · arxiv updated 2019/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
To each pair consisting of a saturated fusion system over a p-group together with a compatible family of Külshammer-Puig cohomology classes, one can count weights in a hypothetical block algebra arising from these data. When the pair arises from a bonafide block of a finite group algebra in characteristic p, the number of conjugacy classes of weights is supposed to be the number of simple modules in the block. We show that there is unique such pair associated with each Benson-Solomon exotic fusion system, and that the number of weights in a hypothetical Benson-Solomon block is 12, independently of the field of definition. This is carried out in part by listing explicitly up to conjugacy all centric radical subgroups and their outer automorphism groups in these systems.