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.
Cohomology theory of averaging algebras, $L_\infty$-structures and homotopy averaging algebras
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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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Cohomology, Homotopy, Extensions, and Automorphisms of Nijenhuis Lie Conformal Algebras
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.