The multigraded Nijenhuis-Richardson Algebra, its universal property and application

Abstract

We define two $(n+1)$ graded Lie brackets on spaces of multilinear mappings. The first one is able to recognize $n$-graded associative algebras and their modules and gives immediately the correct differential for Hochschild cohomology. The second one recognizes $n$-graded Lie algebra structures and their modules and gives rise to the notion of Chevalley cohomology.

Cited by in corpus (3)

• n-ary Lie and Associative Algebras
• The Frölicher-Nijenhuis bracket for derivation based non commutative differential forms
• Cohomology and Versal Deformations of Hom-Leibniz algebras