A hermitian analogue of the Morita theorems. Issue 6 (3rd June 2017) - Dasgupta, Bhanumati; Dasgupta, Soura
ABSTRACT: Let F 1 be an equivalence of type I between two categories of modules with hermitian forms. In other words, suppose F is an equivalence between the two underlying categories of modules, and F 1 is an equivalence, given byF 1 ( M, h ) = ( F ( M ), h F 1 ) and F 1 ( f ) =  F ( f ), such that the non-singularity of a free hyperbolic module of hyperbolic rank 1 is preserved by F 1 . Then every equivalence generated by a set of hermitian Morita equivalence data is of type I and every equivalence of type I arises from a set of hermitian Morita equivalence data.