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.

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

2014 ◽  
Vol 14 (03) ◽  
pp. 1550030 ◽  
Author(s):  
Adam Chapman
Keyword(s):  
Quadratic Forms ◽  
Symplectic Group ◽  
Tensor Products ◽  
Base Field ◽  
Quaternion Algebras ◽  
Characteristic 2

We present a set of generators for the symplectic group which is different from the well-known set of transvections, from which the chain equivalence for quadratic forms in characteristic 2 is an immediate result. Based on the chain equivalences for quadratic forms, both in characteristic 2 and not 2, we provide chain equivalences for tensor products of quaternion algebras over fields with no nontrivial 3-fold Pfister forms. The chain equivalence for biquaternion algebras in characteristic 2 is also obtained in this process, without any assumption on the base-field.

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.

Sign in / Sign up

Export Citation Format

Share Document