Triality Groups Associated with Triple Systems and their Homotope Algebras

Noriaki Kamiya

doi:10.2478/amsil-2021-0001

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Triality Groups Associated with Triple Systems and their Homotope Algebras

Annales Mathematicae Silesianae

Volume 35 (2021): Issue 2 (September 2021)

By: Noriaki Kamiya

Open Access

|Apr 2021

Abstract

We introduce the notion of an (α, β, γ) triple system, which generalizes the familiar generalized Jordan triple system related to a construction of simple Lie algebras. We then discuss its realization by considering some bilinear algebras and vice versa. Next, as a new concept, we study triality relations (a triality group and a triality derivation) associated with these triple systems; the relations are a generalization of the automorphisms and derivations of the triple systems. Also, we provide examples of several involutive triple systems with a tripotent element.

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Articles in this issue

DOI: https://doi.org/10.2478/amsil-2021-0001 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107

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Language: English

Page range: 184 - 210

Submitted on: Oct 21, 2020

Accepted on: Feb 3, 2021

Published on: Apr 13, 2021

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

) triple systems,

Freudenthal–Kantor triple systems,

triality relations,

generalization of automorphisms and derivations

Related subjects:

Mathematics,

General mathematics

© 2021 Noriaki Kamiya, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 35 (2021): Issue 2 (September 2021)