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

Pierre Lecomte·Peter W. Michor·Hubert Schicketanz
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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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Pierre Lecomte, Peter W. Michor, Hubert Schicketanz. 1992-01-01. The multigraded Nijenhuis-Richardson Algebra, its universal property and application. https://arxiv.org/abs/math/9201257

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