Homology, Homotopy and Applications
Volume 18 (2016)
An alternate approach to the Lie bracket on Hochschild cohomology
Pages: 265 – 285
We define Gerstenhaber’s graded Lie bracket directly on complexes other than the bar complex, under some conditions, resulting in a practical technique for explicit computations. The Koszul complex of a Koszul algebra in particular satisfies our conditions. As examples we recover the Schouten–Nijenhuis bracket for a polynomial ring and the Gerstenhaber bracket for a group algebra of a cyclic group of prime order.
Hochschild cohomology, Gerstenhaber bracket, Koszul algebra
2010 Mathematics Subject Classification
16E40, 16S37, 18G10