4 papers
Affinization of algebraic structures: Poisson algebras
Tomasz Brzeziński, Krzysztof Radziszewski, Brais Ramos Pérez
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 multiplica…
Affinization of algebraic structures: Leibniz algebras
Tomasz Brzeziński, Krzysztof Radziszewski, Brais Ramos Pérez
A general procedure of affinization of linear algebra structures is illustrated by the case of Leibniz algebras. Specifically, the definition of an affine Leibniz bracket, that is,…
Lie affgebras vis-à-vis Lie algebras
Ryszard R. Andruszkiewicz, Tomasz Brzeziński, Krzysztof Radziszewski
It is shown that any Lie affgebra, that is an algebraic system consisting of an affine space together with a bi-affine bracket satisfying affine versions of the antisymmetry and Ja…
On matrix Lie affgebras
Tomasz Brzeziński, Krzysztof Radziszewski
Lie brackets or Lie affgebra structures on several classes of affine spaces of matrices are studied. These include general normalised affine matrices, special normalised affine mat…