International Journal of Mathematics and Mathematical Sciences
Volume 1 (1978), Issue 3, Pages 297-305

Equivalence classes of the 3rd Grassman space over a 5-dimensional vector space

Kuldip Singh

Department of Mathematics, The University of New Brunswick, Frederlcton E3B 5A3, N.B., Canada

Received 10 June 1977

Copyright © 1978 Kuldip Singh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An equivalence relation is defined on ΛrV, the rth Grassman space over V and the problem of the determnation of the equivalence classes defined by this relation is considered. For any r and V, the decomposable elements form an equivalence class. For r=2, the length of the element determines the equivalence class that it is in. Elements of the same length are equivalent, those of unequal lengths are inequivalent. When r3, the length is no longer a sufficient indicator, except when the length is one. Besides these general questions, the equivalence classes of Λ3V, when dimV=5 are determined.