On Triality and Pre-structurable Algebras (New contact points of algebraic systems, logics, languages, and computer sciences)
Year: 2015
Type: article
Abstract: We discuss a concept of pre-structurable Algebras based upon triality relations and study its relation to structurable algebra introduced by Allison, as well as to Lie algebras satisfying triality.And this note is an announcement of new results. I Introduction, preliminary and pre-structurable algebraThe structurable algebra [A], which is a class of nonassociative algebras has many interesting proper- ties.First, it satisfies a triality relation [A-F].Moreover, we can construct a Lie algebra $L$ (see [A-F]) that any simple classical Lie algebra can be constructed from some appropriate structurable algebra.Further any such Lie algebra $L$ is invariant under the symmetric group $S_{4}$ and is a $BC_{1}$ -graded Lie algebra of type $B_{1}$ (see [E-O.2] and [E-K-O]).Although the structurable algebra has been originally defined in term of Kantor's triple system [Kan],
Source: 数理解析研究所講究録
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2289103456