On projective representations of Plesken Lie algebras

TL;DR

This paper explores the projective representations of Plesken Lie algebras, establishing a correspondence with their central extensions and second cohomology groups, thus advancing understanding of their algebraic structure.

Contribution

It provides a detailed description of projective representations and central extensions of Plesken Lie algebras, revealing a bijective relationship with second cohomology groups.

Findings

Established a correspondence between second cohomology and central extensions.

Described projective representations of Plesken Lie algebras.

Linked projective equivalence with algebraic cohomology.

Abstract

In this article we describe the projective representation of Plesken Lie algebras and equivalent central extensions of these algebras. Further it is also shown that there exists a bijective correspondence between second cohomology group, equivalent central extensions and projectively equivalent projective representations of Plesken Lie algebras.