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arXiv · 1908.09192

Deformation cohomology of Schur-Weyl categories. Free symmetric categories

Alexei Davydov·Mohamed Elbehiry
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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.

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Alexei Davydov, Mohamed Elbehiry. 2019-08-24. Deformation cohomology of Schur-Weyl categories. Free symmetric categories. https://arxiv.org/abs/1908.09192

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