Four Dimensional Homogeneous Algebras

MacDougall, James A. and Sweet, L. G. (1987) Four Dimensional Homogeneous Algebras. Pacific Journal of Mathematics, 129 . pp. 375-383.

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    An algebra is homogeneous if the automorphism group acts transitively on the one dimensional subspaces of the algebra. The purpose of this paper is to determine all homogeneous algebras of dimension 4. It continues previous work of the authors in which all homogeneous algebras of dimensions 2 and 3 were described. Our main result is the proof that the field must be $GF(2)$ and the algebras are of a type previously described by Kostrikin. There are 5 non-isomorphic algebras of dimension 4; a description of each is given and the automorphism group is calculated in each case.

    Item Type: Article
    Subjects: 00-xx General
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    Depositing User: Stephanie
    Date Deposited: 18 Nov 2010 12:06
    Last Modified: 18 Nov 2010 12:07

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