Takesaki's duality for a non-degenerate co-action.

Katayama, Yoshikazu

doi:10.7146/math.scand.a-12072

Cited by 57 publications

(71 citation statements)

References 2 publications

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“…For our twisted crossed products to be useful, it is important that they have properties like those of ordinary crossed products: A x Y ,G/N,WG should resemble Ax f N. As evidence that this is the case, we show that there is a duality theorem like that of Katayama [10] for untwisted crossed products: every twisted crossed product A x y ,G/N,wG carries a natural dual action <5 of N such that…”

Section: Formally This Corepresentation Is a Unitary W E Um(a C*(g/mentioning

confidence: 95%

“…As we pointed out in the introduction, the case N = G is not quite as strong as Katayama's duality theorem [10], which gives an isomorphism of…”

Section: {G) Now Suppose (Ti (A) Is a Covariant Representation Of (mentioning

confidence: 99%

“…Consider, for example, the crossed product A x s G by a coaction of a simplyconnected solvable Lie group G. Such a group is an iterated semidirect product by copies of D&, and thus we can apply (5.1) repeatedly with N = QL Connes' Thorn isomorphism [5] asserts that K*((A x s G) x N) is then isomorphic to K t+I (A x s G), and hence we can deduce that KM x s G) = K t _ dimG (A). Alternatively, we can first apply Katayama's duality theorem [10] …”

Section: Concluding Remarks Section 5(a)mentioning

confidence: 99%

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Twisted crossed products by coactions

Phillips

Raeburn

1994

J Aust Math Soc A

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We consider coactions of a locally compact group G on a C*-algebra A, and the associated crossed product C*-algebra A x G. Given a normal subgroup N of G, we seek to decompose A x G as an iterated crossed product (A x G/N) x N, and introduce notions of twisted coaction and twisted crossed product which make this possible. We then prove a duality theorem for these twisted crossed products, and discuss how our results might be used, especially when N is abelian.

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Section: Formally This Corepresentation Is a Unitary W E Um(a C*(g/mentioning

confidence: 95%

“…As we pointed out in the introduction, the case N = G is not quite as strong as Katayama's duality theorem [10], which gives an isomorphism of…”

Section: {G) Now Suppose (Ti (A) Is a Covariant Representation Of (mentioning

confidence: 99%

Section: Concluding Remarks Section 5(a)mentioning

confidence: 99%

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Twisted crossed products by coactions

Phillips

Raeburn

1994

J Aust Math Soc A

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“…If the groupoid is a (discrete) group this result may be obtained by combining [Q2,Cor. 2.7] and [Kt,Th. 8]; I wish to thank Quigg for bringing this to my attention.…”

Section: ])mentioning

confidence: 99%

Fell bundles over groupoids

Kumjian

1998

Proc. Amer. Math. Soc.

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“…We give a short proof of the analogous result for full crossed products by actions of amenable groups. Also we provide short, elegant proofs of both Katayama and Imai-Takai duality for full crossed products [5,Theorem 4], [3,Theorem 3.6], [11,Theorem 6] (Corollaries 2.6 and 2.12).…”

Section: Introductionmentioning

confidence: 99%

Duality for full crossed products of 𝐶*-algebras by non-amenable groups

Nilsen¹

1998

Proc. Amer. Math. Soc.

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Abstract. Let (A, G, δ) be a cosystem and (A, G, α) be a dynamical system. We examine the extent to which induction and restriction of ideals commute, generalizing some of the results of Gootman and Lazar (1989) to full crossed products by non-amenable groups. We obtain short, new proofs of Katayama and Imai-Takai duality, the faithfulness of the induced regular representation for full coactions and actions by amenable groups. We also give a short proof that the space of dual-invariant ideals in the crossed product is homeomorphic to the space of invariant ideals in the algebra, and give conditions under which the restriction mapping is open.

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Takesaki's duality for a non-degenerate co-action.

Cited by 57 publications

References 2 publications

Twisted crossed products by coactions

Twisted crossed products by coactions

Fell bundles over groupoids

Duality for full crossed products of 𝐶*-algebras by non-amenable groups

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