Bipartite graphs and the structure of finite-dimensional semisimple Leibniz algebras

TL;DR

This paper explores the relationship between bipartite graphs and finite-dimensional semisimple Leibniz algebras, establishing a construction method that characterizes these algebras through graph structures.

Contribution

It introduces a novel construction linking bipartite graphs to indecomposable semisimple Leibniz algebras, providing a new classification approach.

Findings

Finite connected bipartite graphs correspond to indecomposable semisimple Leibniz algebras.

Any such Leibniz algebra can be constructed from a bipartite graph.

The construction offers a new perspective on the structure of Leibniz algebras.

Abstract

Given a finite connected bipartite graph, finite-dimensional indecomposable semisimple Leibniz algebras are constructed. Furthermore, any finite-dimensional indecomposable semisimple Leibniz algebra admits a similar construction.