Vol. 33, No. 1, 1970

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 331: 1  2
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
ℒ− 2 subspaces of Grassmann product spaces

Marion-Josephine Lim

Vol. 33 (1970), No. 1, 167–182
Abstract

The subspaces of the second order Grassmann product space consisting of products of a fixed irreducible length k and zero are interesting not only for their own sake and their usefulness when determining the structure of linear transformations on the product space into itself which preserve the irreducible length k, but also because they are isomorphic to subspaces of skew-symmetric matrices of fixed rank 2k. The structure of these subspaces and the corresponding preservers are known for k = 1, when the underlying field F is algebraically closed. This paper gives a complete characterization of these subspaces when k = 2 and F is algebraically closed. When F is not algebraically closed, these subspaces can be different.

Mathematical Subject Classification 2000
Primary: 15A75
Milestones
Received: 14 April 1969
Revised: 14 April 1969
Published: 1 April 1970
Authors
Marion-Josephine Lim