Para-Kahler hom-Lie algebras

TL;DR

This paper introduces para-Kahler structures on hom-Lie algebras, characterizes them, and explores their relationship with phase spaces, providing examples and new constructions in the field of algebraic structures.

Contribution

It defines and characterizes para-Kahler hom-Lie algebras and establishes their connection with phase spaces, offering new methods to construct these structures.

Findings

Para-Kahler hom-Lie algebras can be characterized by specific structures.

A phase space can be constructed from a para-Kahler hom-Lie algebra.

Conversely, phase spaces can be used to build para-Kahler hom-Lie algebras.

Abstract

In this paper, we introduce the notions of pseudo-Riemannian, para-Hermitian and para- Kahler structures on hom-Lie algebras. In addition, we present the characterization of these structures. Also, we provide an example including these structures. We then introduce the phase space of a hom-Lie algebra and using the hom-left symmetric product, we show that a para-Kahler hom-Lie algebra gives a phase space and conversely, we can construct a para-Kahler hom-Lie algebra using a phase space.