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A Note on the Length of Trivectors

Published online by Cambridge University Press:  20 November 2018

J. A. MacDougall
J. A. MacDougall*
Affiliation:
Department of Mathematics, University of Prince Edward Island, Charlottetown, Prince Edward Island
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This note concerns elements (called trivectors) of the third Grassmann product of a complex vector space U. Usually there are many ways to write a given trivector as the sum of simple or decomposable trivectors, and it is an interesting problem to find those representations which contain the smallest possible number of decomposables. This number we shall call the length of the trivector. Let N(n) denote the length of the longest trivector in ∧3U where U has dimension n. In this note we give upper bounds for N(n) when n ≤ 8.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 21 , Issue 3 , 01 September 1978 , pp. 371 - 372
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Capdevielle, Bernadette, Classifications des Formes Trilinéaires Alternées en Dimension 6, Enseign. Math., t. 18, 1972-73, pp. 225-243.Google Scholar
2. Gurevich, G. B., Sur Les Trivecteurs Dans l′Espace à Sept Dimensions, Dok. Akad. Nauk SSSR III, No. 8-9, 1934, pp. 567-569.Google Scholar
3. Gurevich, G. B., Classification des Trivecteurs Ayant le Rang Huit, Dok. Akad. Nauk SSSR II, No. 5-6, 1935, pp. 355-356.Google Scholar