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arXiv · 2009.11618

Cohomology theory of averaging algebras, $L_\infty$-structures and homotopy averaging algebras

Kai Wang·Guodong Zhou
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Abstract

This paper studies averaging algebras, say, associative algebras endowed with averaging operators. We develop a cohomology theory for averaging algebras and justify it by interpreting lower degree cohomology groups as formal deformations and abelian extensions of averaging algebras. We make explicit the $L_\infty$-algebra structure over the cochain complex defining cohomology groups and introduce the notion of homotopy averaging algebras as Maurer-Cartan elements of this $L_\infty$-algebra.

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Kai Wang, Guodong Zhou. 2020-09-24. Cohomology theory of averaging algebras, $L_\infty$-structures and homotopy averaging algebras. https://arxiv.org/abs/2009.11618

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