<abstract xmlns="http://www.w3.org/1999/xhtml"><p>We introduce the notion of an (<italic>α, β, γ</italic>) 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.</p></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.

Triality Groups Associated with Triple Systems and their Homotope Algebras

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"Triality Groups Associated with Triple Systems and their Homotope Algebras"}

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...

Triality Groups Associated with Triple Systems and their Homotope Algebras

Published Online: Apr 13, 2021

Page range: 184 - 210

Received: Oct 21, 2020

Accepted: Feb 03, 2021

DOI: https://doi.org/10.2478/amsil-2021-0001

Keywords
(, ) triple systems, Freudenthal–Kantor triple systems, triality relations, generalization of automorphisms and derivations

© 2021 Noriaki Kamiya, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Triality Groups Associated with Triple Systems and their Homotope Algebras

Published Online: Apr 13, 2021

Page range: 184 - 210

Received: Oct 21, 2020

Accepted: Feb 03, 2021

DOI: https://doi.org/10.2478/amsil-2021-0001

Keywords(, ) triple systems, Freudenthal–Kantor triple systems, triality relations, generalization of automorphisms and derivations

© 2021 Noriaki Kamiya, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
(, ) triple systems, Freudenthal–Kantor triple systems, triality relations, generalization of automorphisms and derivations