Generalized Unitaries and the Picard Group
摘要
After discussing some basic facts about generalized module maps, we use the representation theory of the algebra of adjointable operators on a Hilbert B-module E to show that the quotient of the group of generalized unitaries on E and its normal subgroup of unitaries on E is a subgroup of the group of automorphisms of the range ideal of E in B. We determine the kernel of the canonical mapping into the Picard group of the range ideal in terms of the group of its quasi inner automorphisms. As a by-product we identify the group of bistrict automorphisms of the algebra of adjointable operators on E modulo inner automorphisms as a subgroup of the (opposite of the) Picard group.
引用
@article{arxiv.math/0511661,
title = {Generalized Unitaries and the Picard Group},
author = {M. Skeide},
journal= {arXiv preprint arXiv:math/0511661},
year = {2013}
}
备注
minor corrections, some parts extended, this version is to appear in Proceedings of the Indian Academy of Sciences