Tits construction of the exceptional simple Lie algebras
Alberto Elduque
TL;DR
This paper reviews extensions of Tits construction using superalgebras, leading to the discovery of new simple modular Lie superalgebras, expanding the understanding of exceptional Lie algebra structures.
Contribution
It introduces extended Tits constructions with superalgebras, resulting in new simple modular Lie superalgebras not previously known.
Findings
Extended Tits construction with Jordan superalgebras
Extended Tits construction with composition superalgebras
Discovery of new simple modular Lie superalgebras
Abstract
The classical Tits construction of the exceptional simple Lie algebras has been extended in a couple of directions by using either Jordan superalgebras or composition superalgebras. These extensions are reviewed here. The outcome has been the discovery of some new simple modular Lie superalgebras.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Algebra and Geometry