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Research Article | Open Access

Universal enveloping Hom-algebras of regular Hom-Poisson algebras

School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
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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 e h ( A ).

Keywords

regular Hom-algebrasinvolutive Hom-algebrasHom-Poisson algebrasHom-Poisson modulesuniversal enveloping Hom-algebras
CLC number: 16S10, 16W10, 17B35, 17B63

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AIMS Mathematics
Volume 7 Issue 4,
April 2022
Pages 5712-5727
DOI: 10.3934/math.2022316

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Hu X. Universal enveloping Hom-algebras of regular Hom-Poisson algebras. AIMS Mathematics, 2022, 7(4): 5712-5727. https://doi.org/10.3934/math.2022316

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Received: 19 November 2021
Revised: 23 December 2021
Accepted: 06 January 2022
Published: 15 April 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)