J. Austral. Math. Soc.
72 (2002), 4756

A decomposition theorem for homogeneous algebras

L. G. Sweet
Department of Mathematics
and Computer Science
University of Prince Edward Island
Charlottetown PEI C1A 4P3
Canada
sweet@upei.ca


and



Abstract

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

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