Gerstenhaber bracket on the Hochschild cohomology via an arbitrary resolution. (English) Zbl 1461.16005
This paper computes the Gerstenhaber bracket on the Hochschild cohomology of an algebra using some arbitrary projective bimodule resolution for it. It is well known that the Hochschild cohomology is a derived invariant. Here, the author gives a short proof of this fact. New formulas for the Connes’ differential on the Hochschild cohomology in the case of symmetric algebra are also given. The applications of these formulas are discussed. The BV structure and the Gerstenhaber bracket on the Hochschild cohomology are finally described.
Reviewer: Angela Gammella-Mathieu (Metz)
MSC:
| 16E05 | Syzygies, resolutions, complexes in associative algebras |
| 16E35 | Derived categories and associative algebras |
| 16E40 | (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) |
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