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Three Dimensional Homogeneous Algebras

MacDougall, James A. and Sweet, L. G. (1978) Three Dimensional Homogeneous Algebras. Pacific Journal of Mathematics, 74 . pp. 153-162.

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    Abstract

    An algebra $A$ is homogeneous if its automorphism group acts transitively on the set of one dimensional subspaces of $A$. In this paper the structure of all three dimensional homogeneous algebra is determined. These fall into three classes: (1) truncated quaternion algebras over formally real Pythagorean fields; (2) an algebra over $GF(2)$ in which $x^2 = x$ for all $x$ in $A$, and (3) two algebras over $GF(2)$ which are generated by each of their nonzero elements. The automorphism group is determined in each case.

    Item Type: Article
    Subjects: 00-xx General
    Faculty: UNSPECIFIED
    Depositing User: Stephanie
    Date Deposited: 18 Nov 2010 12:08
    Last Modified: 18 Nov 2010 12:08
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/847

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