Homotopy G-algebra structure on the cochain complex of hom-type algebras
Apurba Das
TL;DR
This paper demonstrates that the cochain complex of hom-associative algebras naturally admits a homotopy G-algebra structure, leading to a Gerstenhaber algebra structure on their cohomology, with similar results for hom-dialgebras.
Contribution
It introduces a homotopy G-algebra structure on the cochain complex of hom-associative algebras, extending known algebraic structures to this twisted setting.
Findings
Hochschild cochain complex of hom-associative algebra has a homotopy G-algebra structure
Cohomology of hom-associative algebra has a Gerstenhaber algebra structure
Similar structures are found for hom-dialgebras
Abstract
A hom-associative algebra is an algebra whose associativity is twisted by an algebra homomorphism. We show that the Hochschild type cochain complex of a hom-associative algebra carries a homotopy G-algebra structure. As a consequence, we get a Gerstenhaber algebra structure on the cohomology of a hom-associative algebra. We also find similar results for hom-dialgebras.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology