A hermitian analogue of the Morita theorems

ABSTRACT

Let F₁ 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 F₁ is an equivalence, given by $F_1(M,h)=\left(F\right(M),h_{F_1})$ and F₁(f) = F(f), such that the non-singularity of a free hyperbolic module of hyperbolic rank 1 is preserved by F₁. 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.

KEYWORDS:

• Algebras with anti-structure
• equivalence of type I and II
• hermitian forms
• hermitian Morita equivalences
• hermitian Morita II
• hermitian Morita theorems
• involutions

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 15B57
• 16D90

View correction statement:

Erratum of “A Hermitian analogue of the Morita theorems”

Acknowledgments

This work is partially supported by US NSF grants EPS-1101284, CNS-1329657, CCF-1302456 and ONR grant N00014-13-1-0202. We thank the reviewer for his/her meticulous attention to detail, due to which the paper is free of major errors. We thank Dr Wadsworth of UCSD, Dr Weibel of Rutgers University, Dr Reyes, from University of La Laguna, Spain, Dr Unger of University College Dublin and Dr Hahn from the University of Notre Dame for suggestions which enhanced the article.