Deformation cohomology of Schur–Weyl categories

Alexei Davydov ^[1] ; Mohamed Elbehiry ^[2]
1. [1] Ohio University
  
  Ohio University
  
  Township of Athens, Estados Unidos
2. [2] Northeastern University
  
  Northeastern University
  
  City of Boston, Estados Unidos
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 29, Nº. 1, 2023
Idioma: inglés
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Resumen
- The deformation cohomology of a tensor category controls deformations of the constraint 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. The results make precise an intriguing connection between the combinatorics of partitions and invariants of the exterior of the general linear algebra observed by Kostant.