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Homotopy Gerstenhaber structure on deformation complex of a morphism

Dennis V. Borisov
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Abstract

$G_\infty$-structure is shown to exist on the deformation complex of a morphism of associative algebras. The main step of the construction is extension of a $B_\infty$-algebra by an associative algebra. Actions of $B_\infty$-algebras on associative and $B_\infty$-algebras are analyzed, extensions of $B_\infty$-algebras by associative and $B_\infty$-algebras, that they act upon, are constructed. The resulting $G_\infty$-algebra on the deformation complex of a morphism is shown to be quasi-isomorphic to the $G_\infty$-algebra on deformation complex of the corresponding diagram algebra.

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BibTeXRIS

Dennis V. Borisov. 2005-10-11. Homotopy Gerstenhaber structure on deformation complex of a morphism. https://arxiv.org/abs/math/0510210

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