Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

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

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article Article Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]