December 2022 Hom-Poisson-Nijenhuis structures and Hom-Dirac structures
Tomoya Nakamura
Tsukuba J. Math. 46(2): 193-216 (December 2022). DOI: 10.21099/tkbjm/20224602193

Abstract

In this paper, we develop the theory of Hom-Lie algebroids, Hom-Lie bialgebroids and Hom-Courant algebroids introduced by Cai, Liu and Sheng [3]. Specifically, we introduce the notions of Hom-Poisson, Hom-Nijenhuis and Hom-Poisson-Nijenhuis structures on a Hom-Lie algebroid and the notion of Hom-Dirac structures on a Hom-Courant algebroid. We show that there exists a one-to-one correspondence between the pairs consisting of a Poisson structure on $M$ and a Poisson isomorphism for it, and Hom-Poisson structures on $M$ introduced in [3]. Moreover we show that these structures satisfy similar properties to structures non “Hom-”version. For example, there exists the hierarchy of a Hom-Poisson-Nijenhuis structure and we have a relation between Hom-Dirac structures and the Maurer-Cartan type equation.

Citation

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Tomoya Nakamura. "Hom-Poisson-Nijenhuis structures and Hom-Dirac structures." Tsukuba J. Math. 46 (2) 193 - 216, December 2022. https://doi.org/10.21099/tkbjm/20224602193

Information

Published: December 2022
First available in Project Euclid: 17 March 2023

MathSciNet: MR4561578
zbMATH: 1515.53082
Digital Object Identifier: 10.21099/tkbjm/20224602193

Subjects:
Primary: 53D17

Keywords: Courant algebroids , Dirac structures , Hom-Lie algebroids , Lie algebroids , Poisson structures

Rights: Copyright © 2022 University of Tsukuba, Institute of Mathematics

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Vol.46 • No. 2 • December 2022
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