scholarly journals Composition of quadratic forms and tensor product of quaternion algebras

1985 ◽  
Vol 96 (2) ◽  
pp. 347-367 ◽  
Author(s):  
Sergey Yuzvinsky
Keyword(s):  
Tensor Product ◽  
Quadratic Forms ◽  
Quaternion Algebras

scholarly journals Clifford division algebras and anisotropic quadratic forms: two counterexamples

1986 ◽  
Vol 28 (2) ◽  
pp. 227-228 ◽  
Author(s):  
P. Mammone ◽  
J. P. Tignol
Keyword(s):  
Quadratic Form ◽  
Tensor Product ◽  
Division Algebra ◽  
Quadratic Forms ◽  
Division Algebras ◽  
Quaternion Algebras ◽  
Image Position

In a recent paper [3], D. W. Lewis proposed the following conjecture. (The notation is the same as that in [2] and [3].)Conjecture. Let F be a field of characteristic not 2 and let a1, b1…, an, bn ∈ Fx. The tensor product of quaternion algebrasis a division algebra if and only if the quadratic form over Fis anisotropic.This equivalence indeed holds for n = 1 as is well known [2, Theorem 2.7], and Albert [1] (see also [4, §15.7]) has shown that it also holds for n = 2. The aim of this note is to provide counterexamples to both of the implications for n ≥ 3.

scholarly journals On the tensor product of quaternion algebras of characteristic two

1988 ◽  
Vol 30 (1) ◽  
pp. 111-113
Author(s):  
P. Mammone
Keyword(s):  
Tensor Product ◽  
Quadratic Forms ◽  
Sufficient Conditions ◽  
Tensor Products ◽  
Necessary And Sufficient Conditions ◽  
Division Algebras ◽  
Quaternion Algebras ◽  
Characteristic Two ◽  
Necessary And Sufficient

The purpose of this note is to generalize to fields of characteristic two the results obtained in [4]. We obtain necessary and sufficient conditions involving quadratic forms for certain tensor products of quaternion algebras to be division algebras.

scholarly journals Transfer of quadratic forms and of quaternion algebras over quadratic field extensions

2018 ◽  
Vol 111 (2) ◽  
pp. 135-143
Author(s):  
Karim Johannes Becher ◽  
Nicolas Grenier-Boley ◽  
Jean-Pierre Tignol
Keyword(s):  
Quadratic Forms ◽  
Quadratic Field ◽  
Quaternion Algebras ◽  
Field Extensions

27.—Generating Sets for Fuchsian Groups

1975 ◽  
Vol 72 (4) ◽  
pp. 317-326 ◽  
Author(s):  
J. H. H. Chalk ◽  
B. G. A. Kelly
Keyword(s):  
Quadratic Forms ◽  
Fundamental Region ◽  
Fuchsian Groups ◽  
Quaternion Algebras ◽  
Generating Sets ◽  
Complete Set ◽  
Explicit Bounds

SynopsisFor a class of Fuchsian groups, which includes integral automorphs of quadratic forms and unit groups of indefinite quaternion algebras, it is shown that the geometry of a suitably chosen fundamental region leads to explicit bounds for a complete set of generators.

scholarly journals Addendum: "Chain equivalences for symplectic bases, quadratic forms and tensor products of quaternion algebras"

2015 ◽  
Vol 14 (07) ◽  
pp. 1591001
Author(s):  
Adam Chapman
Keyword(s):  
Quadratic Forms ◽  
Tensor Products ◽  
Quaternion Algebras

We show how the chain lemma for quaternion algebras over fields of F ≠ 2 and [Formula: see text] can be strengthened so that up to two slots are changed at a time.

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