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

Abstract

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 r≥3, 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.