Vol. 29, No. 2, 1969

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Rank k Grassmann products

Marion-Josephine Lim

Vol. 29 (1969), No. 2, 367–374

The general question concerning the structure of subspaces of a symmetry class of tensors in which every nonzero element has an irreducible representation as a sum of decomposable (or pure) elements of a given length is as yet largely unanswered. This problem relates to the problem of characterizing the linear transformations on such a symmetry class which map the set of tensors of “irreducible length” k into itself; i.e., preserves the rank k of the tensors. Another related problem is: “Is it possible to obtain algebraic relations involving the components of a tensor which imply it has rank (“Irreducible length”) k, for any positive integer k”?

Mathematical Subject Classification
Primary: 15.90
Received: 10 May 1968
Published: 1 May 1969
Marion-Josephine Lim