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A decomposition theorem for homogeneous algebras

Part of: General nonassociative rings Other nonassociative rings and algebras

Published online by Cambridge University Press:  09 April 2009

L. G. Sweet  and
J. A. Macdougall
L. G. Sweet
Affiliation:
Department of Mathematics, and Computer Science, University of Prince Edward Island, Charlottetown PEI C1A 4P3, Canada e-mail: sweet@upei.ca
J. A. Macdougall
Affiliation:
Department of Mathematics, University of Newcastle, Callaghan NSW 2308, Australia e-mail: mmjam @cc.newcastle.edu.au
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Abstract

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An algebra A is homogeneous if the automorphism group of A acts transitively on the one dimensional subspaces of A. Suppose A is a homogeneous algebra over an infinite field k. Let La denote left multiplication by any nonzero element a ∈ A. Several results are proved concerning the structure of A in terms of La. In particular, it is shown that A decomposes as the direct sum A = ker La Im La. These results are then successfully applied to the problem of classifying the infinite homogeneous algebras of small dimension.

Keywords

Non-associative algebrasautomorphism group

MSC classification

Secondary: 17D99: None of the above, but in this section 17A36: Automorphisms, derivations, other operators
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 72 , Issue 1 , February 2002 , pp. 47 - 56
Copyright
Copyright © Australian Mathematical Society 2002

References

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