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) (KAR id:53692)
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Official URL: http://iopscience.iop.org/article/10.1088/1751-811... |
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 |
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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: | Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science |
Depositing User: | Peter Hydon |
Date Deposited: | 12 Jan 2016 14:55 UTC |
Last Modified: | 16 Nov 2021 10:22 UTC |
Resource URI: | https://kar.kent.ac.uk/id/eprint/53692 (The current URI for this page, for reference purposes) |
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