Analgous to Hochschild cohomology, we define the singular Hochschild cohomology of an algebra as the Yoneda algebra of the identity bimodule in the singularity category of bimodules. The singularity category was introduced by Buchweitz in 1986 and then rediscovered by Orlov in 2003. In this talk, we construct a natural complex to compute the singular Hochschild cohomology. We prove that this complex carries a natural B-infinity algebra structure. In particular, the singular Hochschild cohomology is a Gerstenhaber algebra. We will also talk about Keller’s recent theorem and conjecture for singular Hochschild cohomology.
B-infinity algebra structure on singular Hochschild cohomology
Oct. 15, 2020 1pm (Zoom (vir…
Rep Theory
Naoki Genra (University of Alberta)
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Screening operators are useful tools to characterize free field realizations of vertex algebras, and give new perspectives in the structures of them. We explain screening operators of the beta-gamma system, affine vertex (super)algebras and W-(super)algebras. We also explain the applications to the coset constructions, representations and trialities of W-algebras.
B-infinity algebra structure on singular Hochschild cohomology