Generalized Unitaries and the Picard Group

Proceedings Mathematical Sciences

Michael Skeide¹ 

[1] Dipartimento S.E.G.e S., Università degli Studi del Molise, Via de Sanctis, 00 Campobasso, Italy$$

关键词: Hilbert modules;    automorphisms;    representations.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

After discussing some basic facts about generalized module maps, we use the representation theory of the algebra $mathscr{B}^a(E)$ of adjointable operators on a Hilbert $mathcal{B}$-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 $mathcal{B}_E$ of 𝐸 in $mathcal{B}$. We determine the kernel of the canonical mapping into the Picard group of $mathcal{B}_E$ in terms of the group of quasi inner automorphisms of $mathcal{B}_E$. 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.

【 授权许可】

Unknown