HNN-extension of Lie superalgebras
Manuel Ladra, Pilar P\'aez-Guill\'an, Chia Zargeh
TL;DR
This paper introduces HNN-extensions for Lie superalgebras, demonstrating their embedding properties and applying this to embed any countably dimensional Lie superalgebra into a two-generator one.
Contribution
It develops the theory of HNN-extensions for Lie superalgebras and shows their utility in embedding problems, a novel approach in the field.
Findings
Every Lie superalgebra embeds into its HNN-extension.
Any countably dimensional Lie superalgebra embeds into a two-generator Lie superalgebra.
Abstract
We construct HNN-extensions of Lie superalgebras and prove that every Lie superalgebra embeds into any of its HNN-extensions. Then as an application we show that any Lie superalgebra with at most countable dimension embeds into a two-generator Lie superalgebra.
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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Advanced Algebra and Logic