The automorphism group of a composition of quadratic forms
Author:
C. Riehm
Journal:
Trans. Amer. Math. Soc. 269 (1982), 403-414
MSC:
Primary 10C05; Secondary 10C04, 20F28
DOI:
https://doi.org/10.1090/S0002-9947-1982-0637698-2
MathSciNet review:
637698
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Abstract | References | Similar Articles | Additional Information
Abstract: Let be a (bilinear) composition
of two quadratic spaces
and
over a field
of characteristic
and assume there is a vector in
which induces the identity map on
via this composition. Define
to be the subgroup of
consisting of those pairs
satisfying
identically and define
to be the projection of
on
. The group
is investigated and in particular it is shown that its connected component, as an algebraic group, is isogenous to a product of two or three classical groups and so is reductive. Necessary and sufficient conditions are given for
to be transitive on the unit sphere of
when
and
are Euclidean spaces.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1982-0637698-2
Keywords:
Quadratic forms,
composition of quadratic forms,
algebraic groups,
nilmanifolds
Article copyright:
© Copyright 1982
American Mathematical Society