Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 7 (2012), 69 -- 103

DIFFERENT VERSIONS OF THE IMPRIMITIVITY THEOREM

Tania-Luminiţa Costache

Abstract. 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 [26] and its projective version [29]. Then we remind Mackey's fundamental imprimitivity theorem in the bundle context [14]. Section 5 is dedicated to the imprimitivity theorem for systems of G-covariance [6]. In Section 6 and 7 we refer to the imprimitivity theorem in the context of C* -algebras [39] and to the symmetric imprimitivity theorem [36], [42], [11].

2010 Mathematics Subject Classification: 22D05; 22D10; 20C25; 22D30; 55R10; 57S17; 46L05; 46L35.
Keywords: unitary representation of a locally compact group; projective representation; induced representation; fiber bundle; system of imprimitivity; Morita equivalence.

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Tania-Luminiţa Costache
Faculty of Applied Sciences, University "Politehnica" of Bucharest,
Splaiul Independentei 313, Bucharest, Romania.
e-mail: lumycos1@yahoo.com

http://www.utgjiu.ro/math/sma