Monoidal Categories and the Gerstenhaber Bracket in Hochschild Cohomology

  title={Monoidal Categories and the Gerstenhaber Bracket in Hochschild Cohomology},
  author={Reiner Hermann},
Let A be an associative and unital algebra over a commutative ring K, such that A is K-projective. The Hochschild cohomology ring HH*(A) of A is, as a graded algebra, isomorphic to the Ext-algebra of A in the category of A-bimodules. In 1963, M. Gerstenhaber established a graded Lie bracket on HH*(A) of degree -1 which he described in terms of the so called bar resolution. While the multiplication admits an intrinsic description (Yoneda product), this Lie bracket has resisted such an… 

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