2003
DOI: 10.1007/bf02829631
|View full text |Cite
|
Sign up to set email alerts
|

Pfister involutions

Abstract: The question of the existence of an analogue, in the framework of central simple algebras with involution, of the notion of Pfister form is raised. In particular, algebras with orthogonal involution which split as a tensor product of quaternion algebras with involution are studied. It is proven that, up to degree 16, over any extension over which the algebra splits, the involution is adjoint to a Pfister form. Moreover, cohomological invariants of those algebras with involution are discussed.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
5

Citation Types

0
33
0

Year Published

2007
2007
2016
2016

Publication Types

Select...
5
1

Relationship

0
6

Authors

Journals

citations
Cited by 24 publications
(33 citation statements)
references
References 11 publications
0
33
0
Order By: Relevance
“…The implication (1) ⇒ (3), and the equivalence (2) ⇔ (3), follows from the Pfister Factor Conjecture and the non-hyperbolic splitting result of [8]. The converse implication, (2) or (3) ⇒ (1), is still open in general.…”
Section: Introductionmentioning
confidence: 99%
See 3 more Smart Citations
“…The implication (1) ⇒ (3), and the equivalence (2) ⇔ (3), follows from the Pfister Factor Conjecture and the non-hyperbolic splitting result of [8]. The converse implication, (2) or (3) ⇒ (1), is still open in general.…”
Section: Introductionmentioning
confidence: 99%
“…Assuming that the characteristic of F is different from 2, in [2] it is asked whether the following are equivalent:…”
Section: Introductionmentioning
confidence: 99%
See 2 more Smart Citations
“…Over fields of characteristic different from two, the adjoint involution of a Pfister form is a totally decomposable involution. Pfister forms are a central part of the algebraic theory of quadratic forms, and in [2] it was asked whether totally decomposable involutions share certain characterising properties of Pfister forms. In particular, whether totally decomposable involutions are exactly those involutions on algebras of two-power degree that are either anisotropic or hyperbolic after extending scalars.…”
Section: Introductionmentioning
confidence: 99%