Triangulable Leibniz Algebras
Tiffany Burch, Ernie Stitzinger
TL;DR
This paper extends Lie's theorem to Leibniz algebras, introducing the concept of triangulability and demonstrating its 2-recognizability, which helps identify algebra properties from subalgebras.
Contribution
It generalizes a converse to Lie's theorem for Leibniz algebras and establishes triangulability as a 2-recognizeable property.
Findings
Triangulability is 2-recognizeable for Leibniz algebras.
Triangulability joins solvability and nilpotency as 2-recognizeable properties.
The paper generalizes a converse to Lie's theorem for Leibniz algebras.
Abstract
A converse to Lie's theorem for Leibniz algebras is found and generalized. The result is used to find cases in which the generalized property, called triangulable, is 2-recognizeable; that is, if all 2-generated subalgebras are triangulable, then the algebra is also. Triangulability joins solvability, supersolvability, strong solvability, and nilpotentcy as a 2-recognizeable property for classes of Leibniz algebras.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology