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Closures of Equivalence Classes of Trivectors of an Eight-Dimensional Complex Vector Space

Published online by Cambridge University Press:  20 November 2018

Dragomir Ž. Djoković*
Affiliation:
Rutgers University, New Brunswick, N.J.08903, University of Waterloo, Waterloo, OntarioN2L 3G1
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Abstract

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G. B. Gurevič enumerated all the orbits of GL8(ℂ) in Λ3(ℂ8). There are precisely 23 orbits (including the trivial orbit). For each of these orbits, we determine its closure (for the ordinary topology).

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1983

References

1. Kjoković, D. Ž., Classification of trivectors of an eight-dimensional real vector space to appear in Linear and Multilinear Algebra.Google Scholar
2. Gurevič, G. B., Sur les trivecteurs dans l'éspace à sept dimensions, Dokl. Akad. Nauk SSSR, III (1934), 567-569.Google Scholar
3. Gurevič, G. B., Classifications des trivecteurs ayant le rang huit, Dokl. Akad. Nauk SSSR, II (1935), 355-356.Google Scholar
4. Gurevič, G. B., Foundations of the theory of algebraic invariants, Noordhoff, Groningen 1964.Google Scholar
5. Humphries, J. E., Linear algebraic groups, Springer-Verlag, New York, 1975.Google Scholar
6. Vinberg, E. B. and Elašvili, A. G., Classification of trivectors of a nine-dimensional space, Trudy Sem. Vekt. Tenz. Analizu, M.G.U. No. XVIII (1978), 197-233.Google Scholar