2024/06/26 by Sigiswald Barbier, Barbier, Sigiswald
Mathematics · #18M05 #18M30 (Primary) 17B10 (Secondary) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Finite Group Theory Research #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2406.18436
openalex publication_date 2024/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper introduces monoidal (super)categories resembling the Brauer category. For all categories, we can construct bases of the hom-spaces using Brauer diagrams. These categories include the Brauer category, its deformation the BWM-category, the periplectic Brauer category, and its deformation the periplectic q-Brauer category but also some new exotic categories. We show that the BWM-category is the unique deformation of the Brauer category in this framework, while the periplectic Brauer category has two deformations, which are each other monoidal opposite.