Vol. 59, No. 2, 1975

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 331: 1
Vol. 330: 1  2
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN 1945-5844 (electronic)
ISSN 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
On homogeneous algebras

Lowell G. Sweet

Vol. 59 (1975), No. 2, 585–594
Abstract

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
Milestones
Received: 13 September 1974
Published: 1 August 1975
Authors
Lowell G. Sweet