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CODES, S-STRUCTURES, AND EXCEPTIONAL LIE ALGEBRAS

Part of: Theory of error-correcting codes and error-detecting codes General nonassociative rings Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  07 May 2019

ISABEL CUNHA  and
ALBERTO ELDUQUE Open the ORCID record for ALBERTO ELDUQUE [Opens in a new window]
ISABEL CUNHA
Affiliation:
Departamento de Matemática e Centro de Matemática e Aplicações da Universidade da Beira Interior, Universidade da Beira Interior, 6201-001 Covilhã, Portugale-mail:[email protected]
ALBERTO ELDUQUE
Affiliation:
Departamento de Matemáticas e Instituto Universitario de Matemáticas y Aplicaciones, Universidad de Zaragoza, 50009 Zaragoza, Spaine-mail:[email protected]
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Abstract

The exceptional simple Lie algebras of types E7 and E8 are endowed with optimal $\mathsf{SL}_2^n$ -structures, and are thus described in terms of the corresponding coordinate algebras. These are nonassociative algebras which much resemble the so-called code algebras.

MSC classification

Primary: 17B25: Exceptional (super)algebras
Secondary: 17A30: Algebras satisfying other identities 17B22: Root systems 94B05: Linear codes, general
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 62 , Special Issue S1: Workshop on Nonassociative algebras and their applications , December 2020 , pp. S14 - S27
Copyright
Copyright © Glasgow Mathematical Journal Trust 2019

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