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

In this talk, a bipartite graph associated with a finite-dimensional semisimple Leibniz algebra will be presented. It will be shown that using an arbitrary connected bipartite graph, one can construct an indecomposable semisimple Leibniz algebra, whose associated graph is a given graph. Thus, all finite-dimensional semisimple Leibniz algebras are described using bipartite graphs whose vertices are simple Lie algebras and irreducible finite-dimensional modules over them.