<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

Publié en ligne: 13 avr. 2021

Pages: 184 - 210

Reçu: 21 oct. 2020

Accepté: 03 févr. 2021

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

Mots clés
(, ) 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

Publié en ligne: 13 avr. 2021

Pages: 184 - 210

Reçu: 21 oct. 2020

Accepté: 03 févr. 2021

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

Mots clés(, ) 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.

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