Abstract
Let k be a field of characteristic 0, let C be a finite split category, let α be a 2-cocycle of C with values in the multiplicative group of k, and consider the resulting twisted category algebra A:=kαC. Several interesting algebras arise that way, for instance, the Brauer algebra. Moreover, the category of biset functors over k is equivalent to a module category over a condensed algebra εAε, for an idempotent ε of A. In [2] the authors proved that A is quasi-hereditary (with respect to an explicit partial order ⩽ on the set of irreducible modules), and standard modules were given explicitly. Here, we improve the partial order ⩽ by introducing a coarser order ⊴ leading to the same results on A, but which allows to pass the quasi-heredity result to the condensed algebra εAε describing biset functors, thereby giving a different proof of a quasi-heredity result of Webb, see [21]. The new partial order ⊴ has not been considered before, even in the special cases, and we evaluate it explicitly for the case of biset functors and the Brauer algebra. It also puts further restrictions on the possible composition factors of standard modules.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.