Automorphisms of real Lie algebras of dimension five or less

Fisher, David J., Gray, Robert J., Hydon, Peter E. (2013) Automorphisms of real Lie algebras of dimension five or less. Journal of Physics A: Mathematical and Theoretical, 46 (225204). pp. 1-18. ISSN 1751-8113. E-ISSN 1751-8121. (doi:10.1088/1751-8113/46/22/225204)

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Abstract

The Lie algebra version of the Krull-Schmidt Theorem is formulated and proved. This leads to a method for constructing the automorphisms of a direct sum of Lie algebras from the automorphisms of its indecomposable components. For finite-dimensional Lie algebras, there is a well-known algorithm for finding such components, so the theorem considerably simplifies the problem of classifying the automorphism groups. We illustrate this by classifying the automorphisms of all indecomposable real Lie algebras of dimension five or less. Our results are presented very concisely, in tabular form.

Item Type: Article
DOI/Identification number: 10.1088/1751-8113/46/22/225204
Uncontrolled keywords: Automorphisms, Lie algebras, Krull-Schmidt Theorem
Subjects: Q Science > QA Mathematics (inc Computing science) > QA252 Lie algebras
Q Science > QA Mathematics (inc Computing science) > QA252 Lie algebras

Q Science > QA Mathematics (inc Computing science) > QA387 Basic Lie theory
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Peter Hydon
Date Deposited: 12 Jan 2016 14:55 UTC
Last Modified: 29 May 2019 16:52 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/53692 (The current URI for this page, for reference purposes)
Hydon, Peter E.: https://orcid.org/0000-0002-3732-4813
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