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.
