Self-similar graph $C^*$-algebras and partial crossed products

Suppose that H is a closed subgroup of a locally compact group G. We show that a unitary representation U of H is the restriction of a unitary representation of G if and only if a dual representation Û of a crossed product C*(G) ⋊ (G/H) is regular in an appropriate sense. We then discuss the problem of deciding whether a given representation is regular; we believe that this problem will prove to be an interesting test question in non-Abelian duality for crossed products of C*-algebras.

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Homogeneous C*-algebras whose spectra are tori

Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics ◽

10.1017/s1446788700022576 ◽

1985 ◽

Vol 38 (1) ◽

pp. 9-39 ◽

Cited By ~ 8

Author(s):

Shaun Disney ◽

Iain Raeburn

Keyword(s):

Isomorphism Class ◽

Homotopy Theory ◽

Transformation Group ◽

Crossed Products ◽

C Algebras ◽

Isomorphism Classes ◽

Twisted Group

AbstractBy a theorem of Fell and Tomiyama-Takesaki, an N-homogeneous C*-algebra with spectrum X has the form Γ(E) for some bundle E over X with fibre MN(C), and its isomorphism class is determined by that of E and its pull-backs f*E along homeomorphisms f of X. We describe the homogeneous C*-algebras with spectrum T2 or T3 by classifying the MN-bundles over Tk using elementary homotopy theory. We then use our results to determine the isomorphism classes of a variety of transformation group C*-algebras, twisted group C*-algebras and more general crossed products.

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Crossed products of C-algebras by -endomorphisms

Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics ◽

10.1017/s1446788700037113 ◽

1993 ◽

Vol 54 (2) ◽

pp. 204-212 ◽

Cited By ~ 43

Author(s):

P. J. Stacey

Keyword(s):

Universal Property ◽

Crossed Products ◽

C Algebras ◽

Covariant Representations

AbstractCrossed products of C*-algebras by *-endomorphisms are defined in terms of a universal property for covariant representations implemented by families of isometries and some elementary properties of covariant representations and crossed products are obtained.

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Induced Coactions of Discrete Groups on C*-Algebras

Canadian Journal of Mathematics ◽

10.4153/cjm-1999-032-1 ◽

1999 ◽

Vol 51 (4) ◽

pp. 745-770 ◽

Cited By ~ 4

Author(s):

Siegfried Echterhoff ◽

John Quigg

Keyword(s):

Quotient Group ◽

Discrete Group ◽

Discrete Groups ◽

Crossed Products ◽

C Algebras ◽

Morita Equivalent ◽

Close Relationship

AbstractUsing the close relationship between coactions of discrete groups and Fell bundles, we introduce a procedure for inducing a C*-coaction δ: D → D ⊗C*(G/N) of a quotient group G/N of a discrete group G to a C*-coaction Ind δ: Ind D → D ⊗C*(G) of G. We show that induced coactions behave in many respects similarly to induced actions. In particular, as an analogue of the well known imprimitivity theorem for induced actions we prove that the crossed products Ind D ×IndδG and D ×δG/N are always Morita equivalent. We also obtain nonabelian analogues of a theorem of Olesen and Pedersen which show that there is a duality between induced coactions and twisted actions in the sense of Green. We further investigate amenability of Fell bundles corresponding to induced coactions.

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