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Geometry on formal duals of algebras
A Gerstenhaber algebra is a Poisson 2-algebra, a Poisson algebra in graded vector spaces with Poisson bracket of degree -1.
A Gerstenhaber algebra is a chain complex equipped with
a symmetric product ;
a skew-symmetric bracket ;
such that associativity of and the Jacobi identity for holds and such that is a derivation of .
This is due to Cohen (1976).
Murray Gerstenhaber, The cohomology structure of an associative ring, Ann. of Math., 78 (1963), 267-288 MR28:5102
Ping Xu, Gerstenhaber algebras and BV-algebras in Poisson geometry, Commun. Math. Phys. 200, No.3, 545-560 (1999).
Revised on December 21, 2016 05:01:21
by Urs Schreiber