Vol. 33, No. 1, 1970

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ℒ− 2 subspaces of Grassmann product spaces

Marion-Josephine Lim

Vol. 33 (1970), No. 1, 167–182

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
Received: 14 April 1969
Revised: 14 April 1969
Published: 1 April 1970
Marion-Josephine Lim