The multigraded Nijenhuis-Richardson Algebra, its universal property and application
Pierre Lecomte, Peter W. Michor, Hubert Schicketanz
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.
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