Involutions on Composition Algebras
Involutions on composition algebras over rings where 2
is invertible are investigated. It is proved that there is a one-one
correspondence between non-standard involutions of the first kind, and
composition subalgebras of half rank. Every non-standard involution of
the first kind is isomorphic to the natural generalization of Lewis's
hat-involution. Any involution of the second kind on a composition
algebra C over a quadratic etale R-algebra S can be
written as the tensor product of the standard involution of a unique
R-composition subalgebra of C and the standard involution
of S/R. The latter generalizes a well-known theorem of Albert on
quaternion algebras with unitary involutions.
S. Pumpluen < susanne.pumpluen@mathematik.uni-regensburg.de >