𝐾-theory for generalized Lamplighter groups

Li, Xin

doi:10.1090/proc/14619

Cited by 5 publications

(6 citation statements)

References 14 publications

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“…and where G is a group satisfying BCC. This generalizes the case k 0 = 1 from [Li19]. We denote by gcd(k 0 , .…”

Section: Finite-dimensional Algebrasmentioning

confidence: 92%

“…Building up on the work in [CEL13], Xin Li [Li19] computed this when A is a finite-dimensional C * -algebra of the form C ⊕ 1≤k≤N M p k , assuming the Baum-Connes conjecture with coefficients (referred to as BCC below) for G [BCH94]. His motivation was to compute the K-theory of the reduced group C * -algebra of the wreath product H ≀ G for an arbitrary finite group H. For A = C ⊕ 1≤k≤N M p k , the K-theory groups K * A ⊗G ⋊ r G are computed in [Li19] as…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

$K$-theory of non-commutative Bernoulli Shifts

Chakraborty¹,

Echterhoff²,

Kranz³

et al. 2022

Preprint

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For a large class of C * -algebras A, we calculate the Ktheory of reduced crossed products A ⊗G ⋊r G of Bernoulli shifts by groups satisfying the Baum-Connes conjecture. In particular, we give explicit formulas for finite-dimensional C * -algebras, UHF-algebras, rotation algebras, and several other examples. As an application, we obtain a formula for the K-theory of reduced C * -algebras of wreath products H ≀ G for large classes of groups H and G. Our methods use a generalization of techniques developed by the second named author together with Joachim Cuntz and Xin Li, and a trivialization theorem for finite group actions on UHF algebras developed in a companion paper by the third and fourth named authors.

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“…and where G is a group satisfying BCC. This generalizes the case k 0 = 1 from [Li19]. We denote by gcd(k 0 , .…”

Section: Finite-dimensional Algebrasmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

$K$-theory of non-commutative Bernoulli Shifts

Chakraborty¹,

Echterhoff²,

Kranz³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Thus the K-theory formula derived in this paper generalizes the results in [ 13 , 14 ] from global dynamical systems to partial dynamical systems. The original result in [ 13 , 14 ] leads for instance to a K-theory formula for crossed products attached to topological full shifts, the topological version of Bernoulli shifts (see [ 14 , 36 ]), while our generalization applies to partial dynamical systems arising for instance from tilings where the original result was not applicable.…”

Section: Introductionmentioning

confidence: 99%

K-Theory for Semigroup C*-Algebras and Partial Crossed Products

2021

Commun. Math. Phys.

Self Cite

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Using the Baum–Connes conjecture with coefficients, we develop a K-theory formula for reduced C*-algebras of strongly 0-E-unitary inverse semigroups, or equivalently, for a class of reduced partial crossed products. This generalizes and gives a new proof of previous K-theory results of Cuntz, Echterhoff and the author. Our K-theory formula applies to a rich class of C*-algebras which are generated by partial isometries. For instance, as new applications which could not be treated using previous results, we discuss semigroup C*-algebras of Artin monoids, Baumslag-Solitar monoids and one-relator monoids, as well as C*-algebras generated by right regular representations of semigroups of number-theoretic origin, and C*-algebras attached to tilings.

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“…The objective of this paper is to compute the K -theory group of the reduced crossed product A ⊗G r G in as many cases as possible. Building up on the work in [6], Xin Li [20] computed this when A is a finitedimensional C * -algebra of the form C ⊕ 1≤k≤N M p k , assuming the Baum-Connes conjecture with coefficients (referred to as BCC below) for G [1]. His motivation was to compute the K -theory of the reduced group C * -algebra of the wreath product H G for an arbitrary finite group H .…”

mentioning

confidence: 99%

“…His motivation was to compute the K -theory of the reduced group C * -algebra of the wreath product H G for an arbitrary finite group H . For A = C ⊕ 1≤k≤N M p k , the K -theory groups K * A ⊗G r G are computed in [20] as…”

mentioning

confidence: 99%

K-theory of noncommutative Bernoulli shifts

et al. 2023

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For a large class of $$C^*$$ C ∗ -algebras A, we calculate the K-theory of reduced crossed products $$A^{\otimes G}\rtimes _rG$$ A ⊗ G ⋊ r G of Bernoulli shifts by groups satisfying the Baum–Connes conjecture. In particular, we give explicit formulas for finite-dimensional $$C^*$$ C ∗ -algebras, UHF-algebras, rotation algebras, and several other examples. As an application, we obtain a formula for the K-theory of reduced $$C^*$$ C ∗ -algebras of wreath products $$H\wr G$$ H ≀ G for large classes of groups H and G. Our methods use a generalization of techniques developed by the second named author together with Joachim Cuntz and Xin Li, and a trivialization theorem for finite group actions on UHF algebras developed in a companion paper by the third and fourth named authors.

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𝐾-theory for generalized Lamplighter groups

Abstract: We compute K-theory for the reduced group C*-algebras of generalized Lamplighter groups.

Cited by 5 publications

References 14 publications

$K$-theory of non-commutative Bernoulli Shifts

$K$-theory of non-commutative Bernoulli Shifts

K-Theory for Semigroup C*-Algebras and Partial Crossed Products

K-theory of noncommutative Bernoulli shifts

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