A decomposition theorem for homogeneous algebras



Title A decomposition theorem for homogeneous algebras
Author(s) Lowell G. Sweet, J. A. MacDougall
Journal Journal of the Australian Mathematical Society
Date 2002
Volume 72
Start page 47
End page 56
Abstract 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 L-a denote left mulfiplication by any nonzero element a is an element of A. Several results are proved concerning the structure of A in terms of L-a. In particular, it is shown that A decomposes as the direct sum A = ker L-a circle plus Im L-a. These results are then successfully applied to the problem of classifying the infinite homogeneous algebras of small dimension.

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