Indecomposable objects in Khovanov-Sazdanovic's generalizations of Deligne's interpolation categories
Abstract
Khovanov and Sazdanovic recently introduced symmetric monoidal categories parameterized by rational functions and given by quotients of categories of two-dimensional cobordisms. These categories generalize Deligne's interpolation categories of representations of symmetric groups. In this paper, we classify indecomposable objects and identify the associated graded Grothendieck rings of Khovanov-Sazdanovic's categories through sums of representation categories over crossed products of polynomial rings over a general field. To obtain these results, we introduce associated graded categories for Krull-Schmidt categories with filtrations as a categorification of the associated graded Grothendieck ring, and study field extensions and Galois descent for Krull-Schmidt categories.
Keywords
Cite
@article{arxiv.2106.05798,
title = {Indecomposable objects in Khovanov-Sazdanovic's generalizations of Deligne's interpolation categories},
author = {Johannes Flake and Robert Laugwitz and Sebastian Posur},
journal= {arXiv preprint arXiv:2106.05798},
year = {2023}
}
Comments
52 pages. v2: minor fixes and clarifications