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Zbl 0831.15017
Noui, Lemnouar; Revoy, Philippe
Alternating multilinear forms. (Formes multilinéaires alternées.)
(French)
[J] Ann. Math. Blaise Pascal 1, No.2, 43-69 (1994). ISSN 1259-1734

Let \$E\$ be a finite dimensional \$K\$-vector space. The authors study the action of the linear group \$GL (E)\$ on the space \$\Lambda^p E\$. As \$\Lambda^p E^* \cong (\Lambda^pE)^*\$, there is no difference between alternating forms and \$p\$-vectors. Some authors have studied the case \$p = 3\$ and \$\dim E \le 9\$, over an algebraically closed field in the general case.\par The present authors are still interested in the case \$n = 7\$, they talk about invariants of arithmetical, algebraic and geometric meaning that one may assign to a \$p\$-vector. Then they apply this to the cases \$n = 6\$, \$n = 7\$ giving a complete analysis of the situation. Moreover they give a complete proof of Schouten's classification for \$n = 3\$, \$n = 7\$ and algebraically closed \$K\$ and a precise description for the finite fields case.
[N.I.Osetinski (Moskva)]
MSC 2000:
*15A69 Multilinear algebra

Keywords: vector space; \$p\$-vectors; linear group; alternating forms; Schouten's classification; finite fields

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