Symmetry of Lie algebras associated with (\epsilon,\delta) Freudenthal-Kantor triple systems
Noriaki Kaymiya, Susumu Okubo
TL;DR
This paper investigates the symmetry groups of Lie algebras derived from (,) Freudenthal-Kantor triple systems, revealing SL(2) symmetry for a special case and exploring connections with structurable algebra constructions.
Contribution
It identifies the symmetry group as SL(2) for a specific (,) case and examines the relationship between two methods of constructing Lie algebras from structurable algebras.
Findings
Symmetry group is SL(2) for (,) Freudenthal-Kantor triple systems.
Relationship established between two Lie algebra constructions from structurable algebras.
Analysis of symmetry groups enhances understanding of algebraic structures derived from triple systems.
Abstract
Symmetry group of Lie algebras and superalgebras constructed from (\epsilon,\delta) Freudenthal- Kantor triple systems has been studied. Especially, for a special (\epsilon,\epsilon) Freudenthal- Kantor triple, it is SL(2) group. Also, relationship between two constructions of Lie algebras from structurable algebra has been investigated.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Advanced Algebra and Geometry