(-1,-1)-Balanced Freudenthal Kantor triple systems and noncommutative Jordan algebras
Alberto Elduque (University of Zaragoza), Noriaki Kamiya (The, University of Aizu), Susumu Okubo (University of Rochester)
TL;DR
This paper establishes a connection between (-1,-1)-balanced Freudenthal Kantor triple systems and a class of noncommutative Jordan algebras, classifies simple cases over characteristic zero fields, and explores their algebraic structure.
Contribution
It introduces a new correspondence between specific triple systems and noncommutative Jordan algebras, providing classification results for simple algebras in characteristic zero.
Findings
Classification of simple noncommutative Jordan algebras of this type over characteristic zero fields
Explicit construction of noncommutative Jordan algebras from triple systems
Determination of the triple product by the algebra's binary product
Abstract
A noncommutative Jordan algebra of a specific type is attached to any (-1,-1)-balanced Freudenthal Kantor triple system, in such a way that the triple product in this system is determined by the binary product in the algebra. Over fields of characteristic zero, the simple noncommutative Jordan algebras of this type are classified.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Finite Group Theory Research