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arXiv · 2607.17860

Affinization of algebraic structures: Poisson algebras

Tomasz Brzeziński·Krzysztof Radziszewski·Brais Ramos Pérez
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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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Tomasz Brzeziński, Krzysztof Radziszewski, Brais Ramos Pérez. 2026-07-20. Affinization of algebraic structures: Poisson algebras. https://arxiv.org/abs/2607.17860

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