Author(s):
Beites, Patrícia Damas ; Nicolás, Alejandro ; Córdova Martínez, Alejandra Sarina
Date: 2025
Persistent ID: http://hdl.handle.net/10400.6/19702
Origin: uBibliorum
Project/scholarship:
info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB/00212/2020/PT;
Subject(s): Composition álgebra; Identity; Conservative algebra; Maltsev algebra; Enveloping álgebra; Computational linear algebra; Composition álgebra; Composition álgebra; Identity; Identity; Conservative algebra; Conservative algebra; Maltsev algebra; Maltsev algebra; Enveloping álgebra; Enveloping álgebra; Computational linear algebra; Computational linear algebra
Description
Following a research direction proposed in an earlier work, the ternary octonion algebra O, which is a ternary composition algebra, is considered. By hand and applying computational linear algebra on matrices, 1-identities and 2-identities of O are established. From some of these identities, the non-conservativeness of O and of some of its binary reduced algebras, which are binary standard composition algebras of types II and III, is proved. Also from identities of O, using computational linear algebra based on the representation theory of the symmetric group, ternary enveloping algebras for ternary Maltsev algebras are constructed.
