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Quadratic forms and Azumaya algebras.
In this paper, we give a classification of regulär quadratic forms of rank 3 and rank 4 of discriminant l over any domain R in which 2 is invertible, in terms of certain projective modules overExpand
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Hermitian Analogue of a Theorem of Springer
, with involutions and in fact in a much more general setupSe for algebraic groups. The weak form of Springer’s theorem forhermitian forms was proved by Bayer-Fluckiger and Lenstra in BL andtheExpand
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A classification theorem for Albert algebras
Let k be a field whose characteristic is different *om 2 and 3 and let L/k be a quadratic extension. In this paper we prove that for a fixed, degree 3 central simple algebra B over L with anExpand
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WITT GROUPS OF THE PUNCTURED SPECTRUM OF A 3-DIMENSIONAL REGULAR LOCAL RING AND A PURITY THEOREM
Keywords: quadratic forms ; regular local ring ; punctured ; spectrum ; Gersten conjecture Reference CMA-ARTICLE-1999-002doi:10.1112/S0024610799007103 Record created on 2008-12-16, modified onExpand
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A question on the discriminants of involutions of central division algebras
Let k be a field of characteristic not equal to 2 and D a finite dimensional central simple algebra over k whose class is 2-torsion in the Brauer group Br(k) of k. By classical results of Albert [A,Expand
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Minimum-weight rooted not-necessarily-spanning arborescence problem
TLDR
In this paper, we propose the problem of identifying a minimum-weight rooted not-necessarily-spanning arborescence (MRA) in a directed rooted acyclic graph with weights on arcs. Expand
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On compositions and triality.
In this paper we develop a general theory of compositions for quadratic spaces of rank 8 with trivial Arf and Clifford invariants. Using this theory, and adapting a classical technique of C.Expand
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On the discriminant of an involution
In recent papers [KPS1], [KPS2] and [KPS3] the authors gave some applications of the reduced pfaffian of a central simple algebra with involution or, more generally, of an Azumaya algebra. In [KPS3],Expand
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The Minimum Weight Rooted Arborescence Problem: Weights on ARCS Case
In a rooted acyclic graph, G, there exits, in general, several rooted (not necessarily spanning) arborscences. Depending on whether the graph has weights on nodes, on arcs, or on both, it is possibleExpand
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Tits' Constructions of Jordan Algebras and F4 Bundles on the Plane
In this paper, constructions of Jordan algebras over commutative rings are given which place, within a general set-up, the classical Tits constructions of exceptional central simple Jordan algebrasExpand
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