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An alternative to the Plücker relations


Author: Herbert A. Robinson
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
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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.


References [Enhancements On Off] (What's this?)

  • [1] Robert Grone, Decomposable tensors as a quadratic variety, Proc. Amer. Math. Soc. (to appear). MR 0472853 (57:12542)
  • [2] W. V. D. Hodge and D. Pedoe, Methods of algebraic geometry. I, Cambridge Univ. Press, London and New York, 1968.
  • [3] Marvin Marcus, Finite dimensional multilinear algebra. I, Dekker, New York, 1973. MR 0352112 (50:4599)
  • [4] -, Finite dimensional multilinear algebra. II, Dekker, New York, 1975.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0466185-3
Keywords: Decomposable tensor, Grassmann space, Plücker relations, tensor rank
Article copyright: © Copyright 1977 American Mathematical Society

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