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|
|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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