Quadratic forms of dimension 8 with trivial discriminant and Clifford algebra of index 4

被引：4

作者：

Masquelein, Alexandre ^{[1
]}

Queguiner-Mathieu, Anne ^{[2
]}

Tignol, Jean-Pierre ^{[1
]}

机构：

[1] Univ Catholique Louvain, Dept Math, B-1348 Louvain, Belgium

[2] Univ Paris 12, LAGA, CNRS,UMR 7539, Univ Paris 13,IUFM, F-93430 Villetaneuse, France

来源：

ARCHIV DER MATHEMATIK | 2009年 / 93卷 / 02期

关键词：

Quadratic Form; Tensor Product; Clifford Algebra; Algebra Homomorphism; Quaternion Algebra;

D O I：

10.1007/s00013-009-0019-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Izhboldin and Karpenko proved in Math. Z. (234 (2000), 647-695, Theorem 16.10) that any quadratic form of dimension 8 with trivial discriminant and Clifford algebra of index 4 is isometric to the transfer, with respect to some quadratic ,tale extension, of a quadratic form similar to a two-fold Pfister form. We give a new proof of this result, based on a theorem of decomposability for degree 8 and index 4 algebras with orthogonal involution.

引用

页码：129 / 138

页数：10

共 11 条

[1] Quadratic forms of dimension 8 with trivial discriminant and Clifford algebra of index 4
Alexandre Masquelein
Anne Quéguiner-Mathieu
Jean-Pierre Tignol
[J]. Archiv der Mathematik, 2009, 93 : 129 - 138
[2] 8 dimensional quadratic forms for which the index of the Clifford algebra is 8
Laghribi, A
[J]. K-THEORY, 1997, 12 (04): : 371 - 383
[3] QUADRATIC FORMS AND CLIFFORD ALGEBRA
LABORDE, O
[J]. BULLETIN DES SCIENCES MATHEMATIQUES, 1972, 96 (03): : 199 - &
[4] The Clifford algebra in the theory of algebras, quadratic forms, and classical groups
Hahn, A
[J]. CLIFFORD ALGEBRAS: APPLICATIONS TO MATHEMATICS, PHYSICS, AND ENGINEERING, 2004, 34 : 305 - 322
[5] The isotropy of quadratic forms of dimension <=8 over the function field of a quadric
Laghribi, A
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1996, 323 (05): : 495 - 499
[6] Study on noncommutative Jordan real division algebras of dimension 8, whose Lie derivation algebra is not trivial
Rochdi, A
[J]. JOURNAL OF ALGEBRA, 1995, 178 (03) : 843 - 871
[7] Quaternary even positive definite quadratic forms of discriminant 4p
Chan, WK
[J]. JOURNAL OF NUMBER THEORY, 1999, 76 (02) : 265 - 280
[8] INDECOMPOSABLE RANK-4 QUADRATIC SPACES OF NON-TRIVIAL DISCRIMINANT OVER POLYNOMIAL-RINGS
PARIMALA, R
SRIDHARAN, R
[J]. MATHEMATISCHE ZEITSCHRIFT, 1983, 183 (03) : 281 - 292
[9] On the arithmetic 4-orbifolds associated to integral quaternary quadratic forms of index 2
Montesinos-Amilibia J.M.
[J]. Journal of Geometry, 2017, 108 (3) : 961 - 984
[10] CUSP FORMS IN S4 (Γ0 (79)) AND THE NUMBER OF REPRESENTATIONS OF POSITIVE INTEGERS BY SOME DIRECT SUM OF BINARY QUADRATIC FORMS WITH DISCRIMINANT-79
Kendirli, Baris
[J]. BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2012, 49 (03) : 529 - 572

← 1 2 →