In quadratic form theory over fields, a much studied field invariant is the $u$-invariant, defined as the supremum of the dimensions of anisotropic quadratic forms over the field.
We investigate the corresponding notions of $u$-invariant for hermitian and for skew-hermitian forms
over a division algebra with involution, with a special focus on
skew-hermitian forms over a quaternion algebra with canonical involution.
Under certain conditions on the center of the quaternion algebra, we obtain sharp bounds for this invariant.
Publié le : 2010-02-15
Classification:
hermitian form,
involution,
division algebra,
isotropy,
system of quadratic forms,
discriminant,
Tsen-Lang Theory,
Kneser's Theorem,
local field,
Kaplansky field,
11E04,
11E39,
11E81
@article{1267798507,
author = {Becher, Karim Johannes and Mahmoudi, Mohammad G.},
title = {The orthogonal $u$-invariant of a quaternion algebra},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {17},
number = {1},
year = {2010},
pages = { 181-192},
language = {en},
url = {http://dml.mathdoc.fr/item/1267798507}
}
Becher, Karim Johannes; Mahmoudi, Mohammad G. The orthogonal $u$-invariant of a quaternion algebra. Bull. Belg. Math. Soc. Simon Stevin, Tome 17 (2010) no. 1, pp. 181-192. http://gdmltest.u-ga.fr/item/1267798507/