Different versions of the imprimitivity theorem

Surveys in Mathematics and its Applications

Tania-Luminiţa Costache¹ 

[1] Faculty of Applied Sciences, University "Politehnica" of Bucharest, Romania;

关键词: unitary representation of a locally compact group;    projective representation;    induced representation;    fiber bundle;    system of imprimitivity;    Morita equivalence;   

DOI  :  

来源: DOAJ

【 摘 要 】

In this paper we present different versions of the imprimitivity theorem hoping that this might become a support for the ones who are interested in the subject. We start with Mackey's theorem [G.W. Mackey, Imprimitivity for representations of locally compact groups I, Proc. Nat. Acad. Sci. USA 35 (1949)] and its projective version [G.W. Mackey, Unitary representations of group extensions, I, Acta Math. 99 (1958)]. Then we remind Mackey's fundamental imprimitivity theorem in the bundle context [J. M. G. Fell, An extension of Mackey's method to Banach * -algebras bundles, Memoir Amer. Math. Soc., 90 (1969)]. Section 5 is dedicated to the imprimitivity theorem for systems of G-covariance [U. Cattaneo, On Mackey's imprimitivity theorem, Comment. Math. Helvetici 54 (1979)]. In Section 6 and 7 we refer to the imprimitivity theorem in the context of C* -algebras [M. A. Rieffel, Induced representations of C* -algebras, Adv. Math. 13 (1974)] and to the symmetric imprimitivity theorem [I. Raeburn, Induced C* -algebras and a symmetric imprimitivity theorem, Math. Ann. 280 (1988)], [D. Williams, Crossed Products of C* -algebras, Mathematical Surveys and Monographs, Vol. 134 (2007)], [S. Echterhoff and I. Raeburn, Induced C* -algebras, coactions and equivariance in the symmetric imprimitivity theorem, Math. Proc. Camb. Phil. Soc. 128 (2000)].

【 授权许可】

Unknown