Generalized unitaries and the Picard group
After discussing some basic facts about generalized module maps, we use the representation theory of the algebra ℬa(E) of adjointable operators on a HilbertB-moduleE to show that the quotient of the group of generalized unitaries onE and its normal subgroup of unitaries onE is a subgroup of the group of automorphisms of the range idealBE ofE inB. We determine the kernel of the canonical mapping into the Picard group ofBE in terms of the group of quasi inner automorphisms ofBE. As a by-product we identify the group of bistrict automorphisms of the algebra of adjointable operators onE modulo inner automorphisms as a subgroup of the (opposite of the) Picard group.
Volume 132, 2022
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