Cohomology theory of averaging algebras, L_∞-structures and homotopy averaging algebras

2020/09/24 by Wang, Kai, Zhou, Guodong
#16E40 16S80 16S70 17B38 #FOS: Mathematics #K-Theory and Homology (math.KT) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2009.11618

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_∞-algebra structure over the cochain complex defining cohomology groups and introduce the notion of homotopy averaging algebras as Maurer-Cartan elements of this L_∞-algebra.

Related

• Controlling structures, deformations and homotopy theory for averaging algebras
• Averaging algebras of any nonzero weight
• Cohomology and Homotopification of averaging operators on the Lie conformal algebras
• An Algebraic Study of Averaging Operators
• 2-term averaging L_∞-algebras and non-abelian extensions of averaging Lie algebras