6 papers
Affinization of algebraic structures: Poisson algebras
Tomasz BrzeziÅski, 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…
Twist deformations for Hopf coquasigroups
Ramón González RodrÃguez, Brais Ramos Pérez
In this paper, we develop a general theory of twist deformations for Hopf coquasigroups in a symmetric monoidal category. To this end, we first introduce and study non-coassociativ…
Opposite brace triples, Hopf braces and matched pairs of Hopf algebras
Ramón González RodrÃguez, Brais Ramos Pérez
In this paper the category of opposite brace triples is introduced in a general braided monoidal setting. Under cocommutativity, it is proved to be isomorphic to the category of Ho…
On modules over a Hopf brace
Ramón González RodrÃguez, Brais Ramos Pérez, Ana Belén RodrÃguez Raposo
Let be a Hopf brace in a symmetric monoidal category . In this article it is proved that the category of modules over is isomorphic…
Affinization of algebraic structures: Leibniz algebras
Tomasz BrzeziÅski, 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,…
Twisted Post-Hopf Algebras, Twisted Relative Rota-Baxter Operators and Hopf Trusses
José Manuel Fernández Vilaboa, Ramón González RodrÃguez, Brais Ramos Pérez
The present article is devoted to studying the categorical relationships between the categories of Hopf trusses, weak twisted post-Hopf algebras, introduced by Wang (2023), and wea…