Involutions on Rectangular Jordan Pairs
Jordan triple systems are equivalent to Jordan pairs with involution.
In recent work with D'Amour on triples of Clifford type we described involutions
on pairs of row and column vectors over a division ring. Generalizing
these results, in this paper we describe all involutions on nondegenerate pairs
of rectangular type A(R,M,f)^J having a simple artinian coordinate algebra R,
or more generally a simple unital coordinate algebra such that the form f is
unital-valued: f(u,v) = 1 for some u in M^+, v in M^-. The involutions are
of "hermitian" type determined by an involution (anti-automorphism s
with s^2 = 1) on the coordinate ring , "automorphism" type determined
by an automorphism s on the coordinate ring with s^2 inner, or of
"isomorphism" type determined by an isomorphism s of the (necessarily
non-artinian) coordinate ring onto a proper subring (with s^2 somewhat
inner).
(This paper has appeared in J. Algebra 225 (2000), 885-903))
K. McCrimmon<kmm4m@weyl.math.Virginia.edu>