Structure of the extended Schrodinger-Virasoro Lie algebra
Shoulan Gao, Cuipo Jiang, Yufeng Pei
TL;DR
This paper investigates the structural properties of the extended Schrodinger-Virasoro Lie algebra, including derivations, central extensions, and automorphisms, revealing its completeness and universal central extension characteristics.
Contribution
It provides a detailed analysis of the derivations, automorphisms, and central extensions, establishing the algebra's completeness and its universal central extension in Leibniz and Lie categories.
Findings
The extended Schrodinger-Virasoro Lie algebra is infinite-dimensional and complete.
The universal central extension in Leibniz and Lie categories coincide.
The algebra's automorphism group and derivations are characterized.
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.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Nonlinear Waves and Solitons