Vol. 35, No. 1, 1970

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Decomposable symmetric tensors

Larry Jean Cummings

Vol. 35 (1970), No. 1, 65–77
Abstract

A k-field is a field over which every polynomial of degree less than or equal to k splits completely. The main theorem characterizes the maximal decomposable subspaces of the k-th symmetric space kV , where V is finite-dimensional vector space over an infinite k-field. They come in three forms: (1) {x1 xk : xk V },x1,,xk1 fixed; (2) a,bk = {x1 xk : xi ∈⟨a,b⟩}; and (3) {x1 xkr ∨⟨a,b(r)},x1, , Xk-r fixed; where a and b are linearly independent vectors in V and a,bis the subspace spanned by a and b.

Mathematical Subject Classification
Primary: 15.85
Milestones
Received: 17 March 1969
Published: 1 October 1970
Authors
Larry Jean Cummings