A decomposition theorem for homogeneous algebras
Description
Citation
| Title | A decomposition theorem for homogeneous algebras |
| Author(s) | L. Sweet, J. MacDougall |
| Journal | Journal of the Australian Mathematical Society |
| Date | 2002 |
| Volume | 72 |
| Issue | |
| 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. |
| ISSN | 1446-7887 |
Using APA 6th Edition citation style.
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