7 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…
Ore meets homothetic extensions
Tomasz Brzeziński, A. T. M. West
Sufficient and necessary conditions for an extension of a skew-derivation of an associative -algebra to a skew derivation on an extension $S…
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…
Special normalised affine matrices. An example of a Lie affgebra
Tomasz Brzeziński
The affine space of traceless complex matrices in which the sum of all elements in every row and every column is equal to one is presented as an example of an affine space with a L…