English

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}
}