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PreprintCC BY 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{brzezinski2026affinization,
  title = {{Affinization of algebraic structures: Poisson algebras}},
  author = {Tomasz Brzeziński and Krzysztof Radziszewski and Brais Ramos Pérez},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.17860},
  eprint = {2607.17860},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.17860},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Affinization of algebraic structures: Poisson algebras
AU  - Tomasz Brzeziński
AU  - Krzysztof Radziszewski
AU  - Brais Ramos Pérez
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2607.17860
UR  - https://arxiv.org/abs/2607.17860
AB  - 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.
ER  -