Affinization of algebraic structures: Poisson algebras

Tomasz Brzeziński; Krzysztof Radziszewski; Brais Ramos Pérez

Affinization of algebraic structures: Poisson algebras

Rings and Algebras 2026-07-20 v1 Quantum Algebra

Authors: Tomasz Brzeziński , Krzysztof Radziszewski , Brais Ramos Pérez

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.

Keywords

affinization Poisson algebras Poisson affgebras affine spaces Lie brackets

Cite

@article{arxiv.2607.17860,
  title  = {Affinization of algebraic structures: Poisson algebras},
  author = {Tomasz Brzeziński and Krzysztof Radziszewski and Brais Ramos Pérez},
  journal= {arXiv preprint arXiv:2607.17860},
  year   = {2026}
}