Group C*-Algebras and K-Theory

By N. Higson, E. Guentner. 2004

94 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4f8126b2208d57f4876b4c03790ac529a425b67a

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In Algebra and Number Theory

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Citations in the corpus

Maximal and reduced Roe algebras of coarsely embeddable spaces (2011, background): “Our main reference for graded K-theory and E-theory is [10], which in turn refers to the ungraded case covered in [8] for many proofs.”
A Kurosh-type theorem for type II1 factors (2004, methodology): “such kernels is due to Skandalis [Sk] and developed by Higson and Guentner [ HG ].”
The maximal coarse Baum-Connes conjecture for spaces which admit a fibred coarse embedding into Hilbert space (2012, methodology): “))}(gt) = β Wx,{tx(x)(s(x))}(gt) −βWx,{t x(y)(s(y))}(gt) ≤ 1 t ktx(x)(s(x)) −tx(y)(s(y))k ≤ 1 t ρ2(d(x,y)) −→ 0 (t → ∞). It follows from an approximation argument, together with [44](Lemma 7.6) and [18](Lemma 3.2), that for all d ≥ 0, R > 0,r > 0,c > 0,ε > 0, there exists 42 t0 > 1 s”
Complete Descriptions of Intermediate Operator Algebras by Intermediate Extensions of Dynamical Systems (2018, background): “nclusions/embeddings play crucial roles: Connes’s classiﬁcation of injective factors [10] (cf. [44]), Popa’s deformation/rigidity theory [53], [52], the Akemann–Ostrand property for hyperbolic groups [20] (see [45], [48] for signiﬁcant applications), characterizations of C∗- simplicity of discrete g”
Higher index theory for certain expanders and Gromov monster groups I (2010, background): “ons of operators by a uniform amount over the entire sequence (Gf n)n∈N. The maps in diagram 12 above will all be constructed as asymptotic morphisms [5]. The reader is referred to the memoir [5] and [9, 16, 8, 7] for background, and the sources of most of the ideas behind the current section. The D”
Boundary amenability of relatively hyperbolic groups (2005, background): “2 in [HG] that the group Γ satisfying the assumptions of Proposition 12 is in the class C defined in [Oz3] (i.”
Some prime factorization results for type II1 factors (2003, methodology): “Proof. The claims were already proved in Lemma 6.2.8 in [ HG ] except that C ∗”