Structure of the extended Schrodinger-Virasoro Lie algebra

Abstract

In this paper, we study the derivations, the central extensions and the automorphism group of the extended Schrodinger-Virasoro Lie algebra, introduced by J. Unterberger in the context of two-dimensional conformal field theory and statistical physics. Moreover, we show that the extended Schrodinger-Virasoro Lie algebra is an infinite-dimensional complete Lie algebra and the universal central extension of the extended Schrodinger-Virasoro Lie algebra in the category of Leibniz algebras is the same as that in the category of Lie algebras.