Universal enveloping Hom-algebras of regular Hom-Poisson algebras

Xianguo Hu; Xianguo Hu

doi:10.3934/math.2022316

AIMS Mathematics

2022, Volume 7, Issue 4: 5712-5727. doi: 10.3934/math.2022316

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Research article

Universal enveloping Hom-algebras of regular Hom-Poisson algebras

Xianguo Hu ^,

School of Mathematical Sciences, Capital Normal University, Beijing 100048, China

Received: 19 November 2021 Revised: 23 December 2021 Accepted: 06 January 2022 Published: 11 January 2022
MSC : 16S10, 16W10, 17B35, 17B63

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) $.
- regular Hom-algebras,
- involutive Hom-algebras,
- Hom-Poisson algebras,
- Hom-Poisson modules,
- universal enveloping Hom-algebras
Citation: Xianguo Hu. Universal enveloping Hom-algebras of regular Hom-Poisson algebras[J]. AIMS Mathematics, 2022, 7(4): 5712-5727. doi: 10.3934/math.2022316

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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) $.

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