Multiplier representations of discrete groups

Kleppner, Adam

doi:10.1090/s0002-9939-1983-0695278-3

Cited by 5 publications

(2 citation statements)

References 16 publications

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“…Indeed, a theorem of Slawny says that whenever σ A is totally skew in the sense that m ∈ Z k and σ A (m, n) = σ A (n, m) for all n ∈ Z k imply m = 0, the twisted group algebra is simple [39,Theorem 3.7]. (Slawny's result was extended to locally compact groups by Kleppner [20], and subsequently extended further by Green in [16,Proposition 32].) The cocycles σ A are generically totally skew, and in particular whenever the entries a ij of A are independent over the rationals.…”

Section: Thusmentioning

confidence: 99%

Deformations of Fell bundles and twisted graph algebras

Raeburn¹

2016

Math. Proc. Camb. Phil. Soc.

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Abstract. We consider Fell bundles over discrete groups, and the C * -algebra which is universal for representations of the bundle. We define deformations of Fell bundles, which are new Fell bundles with the same underlying Banach bundle but with the multiplication deformed by a two-cocycle on the group. Every graph algebra can be viewed as the C * -algebra of a Fell bundle, and there are are many cocycles of interest with which to deform them. We thus obtain many of the twisted graph algebras of Kumjian, Pask and Sims. We demonstate the utility of our approach to these twisted graph algebras by proving that the deformations associated to different cocycles can be assembled as the fibres of a C * -bundle.

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Section: Thusmentioning

confidence: 99%

Deformations of Fell bundles and twisted graph algebras

Raeburn¹

2016

Math. Proc. Camb. Phil. Soc.

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“…Then the 2-cocycle (in this case also called multiplier) ω is T-valued and ℓ 1 id,ω (G; C) =: ℓ 1 ω (G) is the ω-twisted ℓ 1 -algebra of the group G . The isometric * -morphism θ defined in (2.15) reads now Conditions for a discrete group to have at least one type I ω-representation are in [18,Th. 1], to which we send the interested reader; see also [17].…”

Section: If Z Is a Central Subgroup With G/z Rigidly Symmetric Then G...mentioning

confidence: 99%

Symmetry and inverse closedness for Banach $^*$-algebras associated to discrete groups

Măntoiu¹

2015

Banach J. Math. Anal.

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A discrete group G is called rigidly symmetric if for every C * -algebra A the projective tensor product ℓ 1 (G) ⊗A is a symmetric Banach * -algebra. For such a group we show that the twisted crossed product ℓ 1 α,ω (G; A) is also a symmetric Banach * -algebra, for every twisted action (α, ω) of G in a C * -algebra A . We extend this property to other types of decay, replacing the ℓ 1 -condition. We also make the connection with certain classes of twisted kernels, used in a theory of integral operators involving group 2-cocycles. The algebra of these kernels is studied, both in intrinsic and in represented version. * 2010 Mathematics Subject Classification: Primary 47L65, Secundary 22D15, 47D34, 43A20.

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1988

Pure and Applied Mathematics

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Multiplier representations of discrete groups

Abstract: Abstract. Let o be a multiplier on the discrete group G. Extending theorems of Kaniuth and Thoma to the case of multiplier representations, we determine when the left regular a representation of G has a type I subrepresentation, and when all the a representations of G are type I.

Cited by 5 publications

References 16 publications

Deformations of Fell bundles and twisted graph algebras

Deformations of Fell bundles and twisted graph algebras

Symmetry and inverse closedness for Banach $^*$-algebras associated to discrete groups

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