Deformation cohomology of Schur-Weyl categories. Free symmetric categories
Quantum Algebra
2019-08-27 v1 Category Theory
Abstract
The deformation cohomology of a tensor category controls deformations of its monoidal structure. Here we describe the deformation cohomology of tensor categories generated by one object (the so-called Schur-Weyl categories). Using this description we compute the deformation cohomology of free symmetric tensor categories generated by one object with an algebra of endomorphism free of zero-divisors. We compare the answers with the exterior invariants of the general linear Lie algebra.
Keywords
Cite
@article{arxiv.1908.09192,
title = {Deformation cohomology of Schur-Weyl categories. Free symmetric categories},
author = {Alexei Davydov and Mohamed Elbehiry},
journal= {arXiv preprint arXiv:1908.09192},
year = {2019}
}