Cohomology and deformations of associative superalgebras
R. B. Yadav
TL;DR
This paper extends Gerstenhaber's cohomology framework to associative superalgebras, introducing new algebraic structures and a formal deformation theory specific to the superalgebra context.
Contribution
It generalizes cohomology structures to associative superalgebras and develops a formal deformation theory for them.
Findings
Two multiplications induce graded structures on cohomology
Cohomology forms a graded commutative superalgebra
Cohomology forms a graded Lie superalgebra
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.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology