Hermitian Morita theory and hyperbolic unitary groups (Q1066273)

First, O. T. O'Meara gave a non-standard example of isomorphism between linear groups. Subsequently, L. N. Vaserstein proved that this example also can be viewed as standard under the meaning of Morita-equivalence and conjectured that all isomorphisms are Morita-standard. Recently Lie Fa-an (Chinese, preprint) gave a new type of counter-examples for all ranks n, which means that Morita-standard is not a complete description. However, for hyperbolic unitary groups, the conditions of Morita- equivalence found by the authors supply a good approximation to further determine conditions for an isomorphism to be standard and supply a direction to explore the exceptional type.