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GRADED POISSON STRUCTURES AND SCHOUTEN–NIJENHUIS BRACKET ON ALMOST COMMUTATIVE ALGEBRAS

FERDINAND NGAKEU

Department of Mathematics and Computer Science, University of Douala, P. O. Box 24157 Douala, Cameroon

https://doi.org/10.1142/S0219887812500429Cited by:2 (Source: Crossref)

Abstract

We introduce and study the notion of abelian groups graded Schouten–Nijenhuis bracket on almost commutative algebras and show that any Poisson bracket on such algebras is defined by a graded bivector as in the classical Poisson manifolds. As a particular example, we introduce and study symplectic structures on almost commutative algebras. Our result is a generalization of the ℤ₂-graded (super)-Poisson structures.

Keywords:

AMSC: 18R60, 15A69, 17B75

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