Journal ArticleDOI
The Integral Extension of Isometries of Quadratic Forms Over Local Fields
Reads0
Chats0
TLDR
In this paper, the authors consider the problem of finding necessary and sufficient conditions for the existence of an isometry on a lattice L over the regular quadratic space V that maps v onto w.Abstract:
Let F be a local field with ring of integers 0 and prime ideal π0. If V is a vector space over F, a lattice L in F is defined as an 0-module in the vector space V with the property that the elements of L have bounded denominators in the basis for V. If V is, in addition, a quadratic space, the lattice L then has a quadratic structure superimposed on it. Two lattices on V are then said to be isometric if there is an isometry of V that maps one onto the other. In this paper, we consider the following problem: given two elements, v and w, of the lattice L over the regular quadratic space V, find necessary and sufficient conditions for the existence of an isometry on L that maps v onto w.read more
Citations
More filters
Journal Article
Integral lattices and hyperbolic reflection groups
Rudolf Scharlau,C. Walhorn +1 more
TL;DR: In this article, the authors present conditions générales d'utilisation, i.e., toute utilisation commerciale ou impression systématique is constitutive d'une infraction pénale.
Journal ArticleDOI
Some extensions of Witt's theorem†
TL;DR: In this article, the authors extend Witt's theorem to several kinds of simultaneous isometries of subspaces and show sufficient and necessary conditions for the isometry of generic flags or the simultaneous isometry (subspace, self-dual flag) pairs.
Posted Content
Some Extensions of Witt's Theorem
TL;DR: In this article, the authors extend Witt's theorem to several kinds of simultaneous isometries of subspaces, including the simultaneous isometry of generic flags and self-dual flag pairs.
References
More filters
Book
Introduction to quadratic forms
TL;DR: In this paper, the authors present an abstract theory of quadratic forms over global fields with respect to the Dedekind axioms for S ideal theory of extension fields.