Cohomology and deformations of associative superalgebras

Abstract

In this paper we generalize to associative superalgebras Gerstenhaber's work on cohomology structure of an associative algebra. We introduce two multiplications U and [-,-] on the cochain complex C^*(A;A) of an associative superalgebra A. We prove that these multiplications induce two multiplications on H^*(A;A) and make it graded commutative superalgebra and graded Lie superalgebra, respectively. Moreover, we introduce formal deformation theory of associative superalgebras.