The geometry of weakly-einstein manifolds

Abstract

The aim of the project is to study the categorification of some algebraic structures that play an innovative role in mathematics and physics. In concrete, we will investigate Lie and Leibniz algebra crossed modules, their braided version and their relation with the Lie group crossed modules. We will study the extension theory of braided Lie algebra crossed modules, using the non-abelian tensor product of algebras of Lie introduced by Ellis, and will investigate the possible description of a Lie functor between the central extensions of Lie group crossed modules and the central extensions of Lie algebra crossed modules, and the realisation of a central extension crossed modules of algebras of Lie as the infinitesimal extension associated to a central extension of crossed modules of Lie groups.The aim of the project is to study the categorification of some algebraic structures that play an innovative role in mathematics and physics. In concrete, we will investigate Lie and Leibniz algebra crossed modules, their braided version and their relation with the Lie group crossed modules. We will study the extension theory of braided Lie algebra crossed modules, using the non-abelian tensor product of algebras of Lie introduced by Ellis, and will investigate the possible description of a Lie functor between the central extensions of Lie group crossed modules and the central extensions of Lie algebra crossed modules, and the realisation of a central extension crossed modules of algebras of Lie as the infinitesimal extension associated to a central extension of crossed modules of Lie groups.