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Graded Lie Agebroids of Poisson Almost Commutative Algebras

Volume 20, Number 2 (2017), 95 - 107

Graded Lie Agebroids of Poisson Almost Commutative Algebras

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Abstract

We introduce and study the notion of abelian groups graded Lie algebroid structures on almost commutative algebras $\CA$ and show that any graded Poisson bracket on $\CA$ induces a graded Lie algebroid structure on the $\CA$-module of 1-forms on $\CA$ as in the classical Poisson manifolds. We also derive from our formalism the graded Poisson cohomology.