Vol. 59, No. 2, 1975

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On homogeneous algebras

Lowell G. Sweet

Vol. 59 (1975), No. 2, 585–594

If A is an algebra over a field K let Aut (A) denote the group of algebra automorphisms of A. Then A is said to be extremely homogeneous if Aut (A) act transitively on A∖{0}. Also A is said to be homogeneous if Aut (A) acts transitively on the one-dimensional subspaces of A. The purpose of this paper is to investigate some of the basic properties of homogeneous algebras. In particular, the alternative homogeneous algebras and the homogeneous algebras of dimension 2 are classified.

All algebras are assumed to be finite dimensional and not necessarily associative.

Mathematical Subject Classification 2000
Primary: 17A99
Received: 13 September 1974
Published: 1 August 1975
Lowell G. Sweet