Derivations of octonion matrix algebras

Harry Petyt

doi:10.1080/00927872.2019.1581212

Derivations of octonion matrix algebras

Harry Petyt^*

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

3 Citations (Scopus)

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Abstract

It is well-known that the exceptional Lie algebras f4 and g2 arise from the octonions as the derivation algebras of the 3 × 3 hermitian and 1 × 1 antihermitian matrices, respectively. Inspired by this, we compute the derivation algebras of the spaces of hermitian and antihermitian matrices over an octonion algebra in all dimensions.

Original language	English
Pages (from-to)	4216-4223
Number of pages	8
Journal	Communications in Algebra
Volume	47
Issue number	10
Early online date	6 Apr 2019
DOIs	https://doi.org/10.1080/00927872.2019.1581212
Publication status	Published - 3 Oct 2019

Keywords

Derivations
exceptional Lie algebras
Hermitian matrices
octonions

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10.1080/00927872.2019.1581212

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This is the accepted author manuscript (AAM). The final published version (version of record) is available online via Taylor & Francis at https://doi.org/10.1080/00927872.2019.1581212 . Please refer to any applicable terms of use of the publisher.
Accepted author manuscript, 151 KBLicence: Other

https://arxiv.org/abs/1809.02222

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title = "Derivations of octonion matrix algebras",

abstract = "It is well-known that the exceptional Lie algebras f4 and g2 arise from the octonions as the derivation algebras of the 3 × 3 hermitian and 1 × 1 antihermitian matrices, respectively. Inspired by this, we compute the derivation algebras of the spaces of hermitian and antihermitian matrices over an octonion algebra in all dimensions.",

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N2 - It is well-known that the exceptional Lie algebras f4 and g2 arise from the octonions as the derivation algebras of the 3 × 3 hermitian and 1 × 1 antihermitian matrices, respectively. Inspired by this, we compute the derivation algebras of the spaces of hermitian and antihermitian matrices over an octonion algebra in all dimensions.

AB - It is well-known that the exceptional Lie algebras f4 and g2 arise from the octonions as the derivation algebras of the 3 × 3 hermitian and 1 × 1 antihermitian matrices, respectively. Inspired by this, we compute the derivation algebras of the spaces of hermitian and antihermitian matrices over an octonion algebra in all dimensions.

KW - Derivations

KW - exceptional Lie algebras

KW - Hermitian matrices

KW - octonions

UR - https://www.scopus.com/pages/publications/85063945890

U2 - 10.1080/00927872.2019.1581212

DO - 10.1080/00927872.2019.1581212

M3 - Article (Academic Journal)

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VL - 47

SP - 4216

EP - 4223

JO - Communications in Algebra

JF - Communications in Algebra

IS - 10

ER -

Derivations of octonion matrix algebras

Abstract

Keywords

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