Hermitian morita theory and hyperbolic unitary groups

Hermitian Morita Theory and Unitary Groups of Modules over Semisimple Artinian Rings

“…The above helps to translate the case of the quadratic field excluded in Theorem 4.1 of Hahn and Li (1985) into the case excluded in Theorem 4.1 of the current article.…”

“…(or totally isotropic Hahn and O'Meara, 1989) subspace or its hyperbolic length, is well defined when h is nondegenerate (Hahn and O'Meara, 1989, p. 316). If V A is g.h then V A is hyperbolic and hyperbolic rank of V A = V A h (Hahn and Li, 1985;6.1.12 of Hahn and O'Meara, 1989).…”

“…Hahn (1982) classifies the isomorphisms in a new way via equivalences of categories of modules and shows as a consequence that the connection between the underlying rings and modules is expressed by Morita Equivalence" (Hahn and Li, 1985). Hahn and Li (1985) uses the hermitian Morita theory of Hahn (1985) and provides an analogue of this result for hyperbolic classical groups. This article does the same for unitary groups of generalized hyperbolic modules over semisimple Artinian rings A .…”

“…Since composites of HMEs are HMEs, it suffices to show that if the arrow F W D is reversed, then it is still induced by an HME and that the conditions on 1 satisfy Theorem 4.1 of Hahn and Li (1985) for Apply Theorem 4.2 of Hahn and Li (1985) instead of 4.1 of Hahn and Li (1985) to obtain the following theorem. (1) There is an HME F:…”

“…For M h ∈ A , let M B be M considered as a B-module via −1 and h x x 1 = h x x 1 . Then defines an HME Hahn and Li (1985), F f is used for F f .…”