A hermitian analogue of the Morita theorems. Issue 6 (3rd June 2017)

• Record Type: Journal Article
• Authors: Dasgupta, Bhanumati; Dasgupta, Soura
• Is Part Of: Communications in algebra. Volume 45:Issue 6(2017)
• Page Start: 2281
• Page End: 2295
• Publication Date: 2017-06-03
• Subjects: Algebras with anti-structure -- equivalence of type I and II -- hermitian forms -- hermitian Morita equivalences -- hermitian Morita II -- hermitian Morita theorems -- involutions; 15B57 -- 16D90; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2016.1233196
• Languages: English
• ISSNs: 0092-7872

Abstract

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.