Universal enveloping Hom-algebras of regular Hom-Poisson algebras

Abstract

In this paper, we introduce universal enveloping Hom-algebras of Hom-Poisson algebras. Some properties of universal enveloping Hom-algebras of regular Hom-Poisson algebras are discussed. Furthermore, in the involutive case, it is proved that the category of involutive Hom-Poisson modules over an involutive Hom-Poisson algebra $ A $ is equivalent to the category of involutive Hom-associative modules over its universal enveloping Hom-algebra $ U_{eh}(A) $.

Keywords

• regular hom-algebras
• involutive hom-algebras
• hom-poisson algebras
• hom-poisson modules
• universal enveloping hom-algebras