Lie triple system central extensions of Lie algebras
Revaz Kurdiani

TL;DR
This paper explores the relationships between universal central extensions of perfect Lie algebras when viewed as Lie triple systems, Leibniz algebras, and Lie algebras, revealing isomorphisms among these extensions.
Contribution
It demonstrates that the universal central extension of a perfect Lie algebra as a Lie triple system aligns with its extensions as Lie or Leibniz algebras, establishing a unifying perspective.
Findings
Lie triple system universal central extension is isomorphic to Lie algebra extension
Lie triple system universal central extension is isomorphic to Leibniz algebra extension
Extensions are equivalent when viewed through appropriate algebraic frameworks
Abstract
Three kinds of universal central extension are considered for a perfect Lie algebra. More precisely, one can consider such a Lie algebra as a Lie triple system, or a Leibniz algebra and construct appropriate central extensions. We show that Lie triple system universal central extension is isomorphic either to Lie or Leibniz algebra universal central extension considered as a Lie triple system in appropriate way.
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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models
