Submission: 2005, Jun 27, revised 2008, Apr 23
In quadratic form theory over fields, a much studied field invariant is the u-invariant, defined as the supremum over 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. Under certain conditions on the center of the quaternion algebra, we obtain sharp bounds for this invariant.
2000 Mathematics Subject Classification: 11E04, 11E39, 11E81
Keywords and Phrases: hermitian form, isotropy, dimension, algebra with involution, $u$-invariant
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