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

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arxiv 2009.11618 v1 pith:MWBQAPM3 submitted 2020-09-24 math.KT math.RAmath.RT

Kai Wang , Guodong Zhou This is my paper · ORCID
classification math.KTmath.RAmath.RT
keywords algebrasaveragingcohomologyinftyalgebragroupshomotopytheory
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras

    math.RA 2025-09 accept novelty 6.0 of 10

    Averaging commutative and cocommutative infinitesimal bialgebras induce special apre-perm bialgebras via a new splitting of perm algebras.

  2. Cohomology, Homotopy, Extensions, and Automorphisms of Nijenhuis Lie Conformal Algebras

    math.RA 2025-05 reject novelty 4.0 of 10

    Nijenhuis Lie conformal algebras are given a cohomology, a 2-term homotopy theory, a classification of non-abelian extensions, and a Wells-type obstruction to automorphism inducibility.

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