Generalized Unitaries and the Picard Group

Details Generalized Unitaries and the Picard Group Generalized Unitaries and the Picard Group

2005-11-27

arxiv.org/abs/math/0511661v2

Mathematics

Operator Algebras

minor corrections, some parts extended, this version is to appear in Proceedings of the Indian Academy of Sciences

Scientific paper

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.

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