报告题目： Singular Hochschild cohomology and Gerstenhaber algebra

报告人：汪正方博士 巴黎七大

时间：6月2日上午10:00-11:00

地点：管理科研楼1518

摘要：Let A be an associative algebra over a commutative ring k such that A is projective as a k-module. Then the Hochschild cohomology HH^m(A, A) can be viewed as the Hom-space Hom_{D^b(A\otimes_k A^{op})}(A, A[m]) in the bounded derived category D^b(A\otimes_k A^{op}). We replace D^b(A\otimes_k A^{op}) by the singular category D_{sg}(A\otimes_k A^{op}), which is the Verdier quotient of D^b(A\otimes_k A^{op}) by the full subcategory Perf(A\otimes_k A^{op}) consisting of  perfect complexes of A\otimes_k A^{op}-modules and define the singular Hochschild cohomology HH_{sg}^m(A, A) to be the Hom-space Hom_{D_{sg}(A\otimes_k A^{op})}(A, A[m]) for any integer m.

     In this talk, we prove that HH_{sg}^*(A, A) has a Gerstenhaber algebra structure. We provide a prop interpretation for this Gerstenhaber algebra (a joint work with G. Zhou).  We will also give several examples on how to compute HH_{sg}^*(A, A) in the case of radical square zero algebras A.

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