scholarly journals Orthogonal involutions and totally singular quadratic forms in characteristic two

2017 ◽  
Vol 154 (3-4) ◽  
pp. 429-440 ◽  
Author(s):  
A.-H. Nokhodkar
Keyword(s):  
Quadratic Forms ◽  
Characteristic Two

Milnor'ory and quadratic forms over fields of characteristic two

1992 ◽  
Vol 20 (4) ◽  
pp. 1087-1107 ◽  
Author(s):  
Roberto Aravire ◽  
Ricardo Baeza
Keyword(s):  
Quadratic Forms ◽  
Characteristic Two

APPLICATIONS OF SYSTEMS OF QUADRATIC FORMS TO GENERALISED QUADRATIC FORMS

2020 ◽  
Vol 102 (3) ◽  
pp. 374-386
Author(s):  
A.-H. NOKHODKAR
Keyword(s):  
Quadratic Form ◽  
Division Algebra ◽  
Quadratic Forms ◽  
Witt Index ◽  
Characteristic Two ◽  
Isometry Class

A system of quadratic forms is associated to every generalised quadratic form over a division algebra with involution of the first kind in characteristic two. It is shown that this system determines the isotropy behaviour and the isometry class of generalised quadratic forms. An application of this construction to the Witt index of generalised quadratic forms is also given.

scholarly journals Classical groups over division rings of characteristic two

1972 ◽  
Vol 7 (2) ◽  
pp. 191-226 ◽  
Author(s):  
William M. Pender ◽  
G.E. Wall
Keyword(s):  
Normal Subgroup ◽  
Quadratic Form ◽  
Division Ring ◽  
Quadratic Forms ◽  
Factor Group ◽  
Classical Groups ◽  
Isometry Groups ◽  
Division Rings ◽  
Characteristic Two

The notion of quadratic form over a field of characteristic two is extended to an arbitrary division ring of characteristic two with an involution of the first kind. The resulting isometry groups are shown to have a simple normal subgroup and the structure of the factor group is calculated. It is indicated how one may define and analyse all the classical groups in a unified manner by means of quadratic forms.

scholarly journals Classical groups over division rings of characteristic two: Corrigenda and an acknowledgement

1972 ◽  
Vol 7 (2) ◽  
pp. 319-319
Author(s):  
William M. Pender
Keyword(s):  
Quadratic Forms ◽  
Clifford Algebras ◽  
Classical Groups ◽  
Division Rings ◽  
Characteristic Two

In my paper [1], part (b) of Lemma 3.4 and the remark following it are incorrect and should be omitted.The isometry P in page 215, line 2, need not be a generator of T(E, q) as asserted, but can be shown to lie in T(E, q).I am indebted to Professor Tits for pointing out that extended ideas of quadratic forms have already appeared in his paper [2] and in Wall's paper [3]. Professor Tits also discusses the corresponding groups and Clifford algebras in detail.

Association schemes of quadratic forms over a finite field of characteristic two

1998 ◽  
Vol 43 (23) ◽  
pp. 1965-1968 ◽  
Author(s):  
Yangxian Wang ◽  
Chunsen Wang ◽  
Changli Ma
Keyword(s):  
Finite Field ◽  
Quadratic Forms ◽  
Association Schemes ◽  
Characteristic Two
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