Matrix Lie Groups as 3-Dimensional Almost Paracontact Almost Paracomplex Riemannian Manifolds

TL;DR

This paper investigates three-dimensional Lie groups with almost paracontact almost paracomplex Riemannian structures, establishing a correspondence between their Lie algebras and explicit matrix representations within each classification class.

Contribution

It provides a detailed classification and explicit matrix representations of three-dimensional Lie groups with these geometric structures, linking algebraic and geometric properties.

Findings

Classification of Lie groups in each basic class

Explicit matrix representations derived

Correspondence between Lie algebra and group structure

Abstract

Lie groups considered as three-dimensional almost paracontact almost paracomplex Riemannian manifolds are investigated. In each basic class of the classification used for the manifolds under consideration, a correspondence is established between the Lie algebra and the explicit matrix representation of its Lie group.