Symmetric bilinear forms, quadratic forms and MilnorK-theory in characteristic two

1982 ◽  
Vol 66 (3) ◽  
pp. 493-510 ◽  
Author(s):  
Kazuya Kato
Keyword(s):  
Quadratic Forms ◽  
Bilinear Forms ◽  
Characteristic Two

Polarization Relations and Dispersion Equations for Anisotropic Moving Media

1979 ◽  
Vol 34 (10) ◽  
pp. 1147-1157 ◽  
Author(s):  
Helmut Hebenstreit ◽  
Kurt Suchy
Keyword(s):  
Quadratic Forms ◽  
Bilinear Forms ◽  
Dispersion Equations ◽  
Left And Right ◽  
Moving Media ◽  
Eigenvectors And Eigenvalues

Abstract For media anisotropic (but not bi-anisotropic) in the comoving frame polarization relations and dispersion equations are derived using bilinear forms and quadratic forms, respectively. Specializations for media electrically anisotropic but magnetically isotropic (or vice versa) are given using (left and right) eigenvectors and eigenvalues of the material tensors.

Decomposition of Witt Rings

1982 ◽  
Vol 34 (6) ◽  
pp. 1276-1302 ◽  
Author(s):  
Andrew B. Carson ◽  
Murray A. Marshall
Keyword(s):  
Quadratic Forms ◽  
Classification Problem ◽  
Bilinear Forms ◽  
Interesting Problem ◽  
Witt Ring ◽  
Witt Rings ◽  
Finite Case ◽  
Characteristic 2 ◽  
Definition Of

We take the definition of a Witt ring to be that given in [13], i.e., it is what is called a strongly representational Witt ring in [8]. The classical example is obtained by considering quadratic forms over a field of characteristic ≠ 2 [17], but Witt rings also arise in studying quadratic forms or symmetric bilinear forms over more general types of rings [5,7, 8, 9]. An interesting problem in the theory is that of classifying Witt rings in case the associated group G is finite. The reduced case, i.e., the case where the nilradical is trivial, is better understood. In particular, the above classification problem is completely solved in this case [4, 12, or 13, Corollary 6.25]. Thus, the emphasis here is on the non-reduced case. Although some of the results given here do not require |G| < ∞, they do require some finiteness assumption. Certainly, the main goal here is to understand the finite case, and in this sense this paper is a continuation of work started by the second author in [13, Chapter 5].

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

scholarly journals Annihilators of quadratic and bilinear forms over fields of characteristic two

2006 ◽  
Vol 299 (1) ◽  
pp. 294-308 ◽  
Author(s):  
R. Aravire ◽  
R. Baeza
Keyword(s):  
Bilinear 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.

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