2026/07/20 by Tomasz Brzeziński, Krzysztof Radziszewski, Brais Ramos Pérez
#math.RA #math.QA
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.