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3 results

  • A decomposition theorem for homogeneous algebras

  • Part of
  • L. G. Sweet, J. A. Macdougall
  • Journal:
    Journal of the Australian Mathematical Society / Volume 72 / Issue 1 / February 2002
    Published online by Cambridge University Press:
    09 April 2009, pp. 47-56
    Print publication:
    February 2002
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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.

  • Resolutions of Associative and Lie Algebras

  • Ron Adin, David Blanc
  • Journal:
    Canadian Mathematical Bulletin / Volume 43 / Issue 1 / 01 March 2000
    Published online by Cambridge University Press:
    20 November 2018, pp. 3-16
    Print publication:
    01 March 2000
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  • Certain canonical resolutions are described for free associative and free Lie algebras in the category of non-associative algebras. These resolutions derive in both cases from geometric objects, which in turn reflect the combinatorics of suitable collections of leaf-labeled trees.