Affinization of algebraic structures: Poisson algebras

arXiv Math

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Abstract

An affinization of the notion of a Poisson algebra is presented.

This is termed a Poisson affgebra and consists of an affine space together with an associative bi-affine multiplication and a bi-affine Lie bracket that acts as an affine derivation for the associative product.

The constructive relation between Poisson affgebras and Poisson algebras is described and several low-dimensional examples are studied in detail.

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Affinization of algebraic structures: Poisson algebras

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