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Full-Text Articles in Social and Behavioral Sciences
Induced C*-Algebras, Coactions And Equivariance In The Symmetric Imprimitivity Theorem, Siegfried Echterhoff, Iain Raeburn
Induced C*-Algebras, Coactions And Equivariance In The Symmetric Imprimitivity Theorem, Siegfried Echterhoff, Iain Raeburn
Faculty of Engineering and Information Sciences - Papers: Part A
The symmetric imprimitivity theorem provides a Morita equivalence between two crossed products of induced C*-algebras and includes as special cases many other important Morita equivalences such as Green's imprimitivity theorem. We show that the symmetric imprimitivity theorem is compatible with various inflated actions and coactions on the crossed products.
Naturality And Induced Representations, Siegfried Echterhoff, S Kaliszewski, John Quigg, Iain Raeburn
Naturality And Induced Representations, Siegfried Echterhoff, S Kaliszewski, John Quigg, Iain Raeburn
Faculty of Engineering and Information Sciences - Papers: Part A
We show that induction of covariant representations for C*-dynamical systems is natural in the sense that it gives a natural transformation between certain crossed-product functors. This involves setting up suitable categories of C*-algebras and dynamical systems, and extending the usual constructions of crossed products to define the appropriate functors. From this point of view, Green's Imprimitivity Theorem identifies the functors for which induction is a natural equivalence. Various special cases of these results have previously been obtained on an ad hoc basis.