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Generalized unitaries and the Picard group

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Abstract

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 idealB E ofE inB. We determine the kernel of the canonical mapping into the Picard group ofB E in terms of the group of quasi inner automorphisms ofB E . 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.

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  1. Dipartimento S.E.G.e S., Università degli Studi del Molise, Via de Sanctis, 86100, Campobasso, Italy

    Michael Skeide

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  1. Michael Skeide
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Correspondence to Michael Skeide.

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Skeide, M. Generalized unitaries and the Picard group. Proc. Indian Acad. Sci. (Math. Sci.) 116, 429–442 (2006). https://doi.org/10.1007/BF02829701

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