Geometric Structures On 3-Dimensional Hom-Lie Algebras

Abstract

Some classes of almost contact structures on 5-dimensional nilpotent Lie algebras were investigated in the literature. On the other hand, there are several generalizations of Lie algebras and their characterizations. In particular, an effective characterization of all Hom-Lie algebras of sl(2) type and construction of all the 3-dimensional Hom-Lie algebras for a class of twisting homomorphisms has been presented. A list of twenty 3-dimensional Hom-Lie algebras has been given. In this paper, we consider some classes of almost contact metric structure on all those twenty 3-dimensional Hom-Lie algebras separately. We study semi-cosymplectic, almost cosymplectic and cosymlectic structures. Moreover, we study K-contact and Sasakian structures on 3-dimensional Hom-Lie algebras.

AMS Classification:

• 17B99
• 53D10

Keywords:

• Cosymplectic structure
• Hom-Lie algebra
• K-contact structure
• Sasakian structure