Abstract:It is shown how to obtain a set of homogeneous, degree m polynomials in $(_m^n)$ indeterminates over a field F so that the associated algebraic variety is the set of decomposable elements in the mth Grassmann space over an n-dimensional vector space over F. The same techniques are used to produce an analogous result for the tensor product of m finite dimensional vector spaces.
- Robert Grone, Decomposable tensors as a quadratic variety, Proc. Amer. Math. Soc. 64 (1977), no. 2, 227–230. MR 472853, DOI 10.1090/S0002-9939-1977-0472853-X W. V. D. Hodge and D. Pedoe, Methods of algebraic geometry. I, Cambridge Univ. Press, London and New York, 1968.
- Marvin Marcus, Finite dimensional multilinear algebra. Part 1, Pure and Applied Mathematics, Vol. 23, Marcel Dekker, Inc., New York, 1973. MR 0352112 —, Finite dimensional multilinear algebra. II, Dekker, New York, 1975.
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 66 (1977), 237-240
- MSC: Primary 15A69; Secondary 14M15, 15A75
- DOI: https://doi.org/10.1090/S0002-9939-1977-0466185-3
- MathSciNet review: 0466185