2022/09/19 by Hou, Bo, Shen, Zhongxi, Zhao, Jun · 1 citation
#FOS: Mathematics #K-Theory and Homology (math.KT) #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2209.08715
We define a cup product on the Hochschild cohomology of an associative conformal algebra A, and show the cup product is graded commutative. We define a graded Lie bracket with the degree -1 on the Hochschild cohomology \HH∗(A) of an associative conformal algebra A, and show that the Lie bracket together with the cup product is a Gerstenhaber algebra on the Hochschild cohomology of an associative conformal algebra. Moreover, we consider the Hochschild cohomology of split extension conformal algebra A⊕M of A with a conformal bimodule M, and show that there exist an algebra homomorphism from \HH∗(A⊕M) to \HH∗(A).