Involutions on Rectangular Jordan Pairs

Jordan triple systems are equivalent to Jordan pairs with involution. In recent work with DʹAmour on triples of Clifford type we described involutions on pairs 1, q(Δ). 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 M+ , v M− . The involutions are of “hermitian” type determined by an involution (anti-automorphism σ with σ2 = 1) on the coordinate ring, “automorphism” type determined by an automorphism σ on the coordinate ring with σ2 inner, or of “isomorphism” type determined by an isomorphism σ of the (necessarily non-artinian) coordinate ring onto a proper subring (with σ2 somewhat inner).