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21
C*algebras of Toeplitz type associated with algebraic number fields, preprint
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Nuclearity of semigroup C*algebras and the connection to amenability
 Advances in Math. 244
, 2013
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Partial crossed product description of the C*algebras associated with integral domains
 Proc. Amer. Math. Soc
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On the group cohomology of the semidirect product Z n ⋊ρ Z/m and a conjecture of AdemGePanPetrosyan
, 2011
"... Consider the semidirect product Z n ⋊ρ Z/m. A conjecture of AdemGePanPetrosyan predicts that the associated LyndonHochschildSerre spectral sequence collapses. We prove this conjecture provided that the Z/maction on Z n is free outside the origin. We disprove the conjecture in general, namely ..."
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Cited by 6 (2 self)
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Consider the semidirect product Z n ⋊ρ Z/m. A conjecture of AdemGePanPetrosyan predicts that the associated LyndonHochschildSerre spectral sequence collapses. We prove this conjecture provided that the Z/maction on Z n is free outside the origin. We disprove the conjecture in general, namely, we give an example with n = 6 and m = 4, where the second differential does not vanish.
The topological Ktheory of certain crystallographic groups
 JOURNAL OF NONCOMMUTATIVE GEOMETRY
, 2010
"... Let Γ be a semidirect product of the form Z n ⋊ρ Z/p where p is primeand the Zpaction ρ on Z n is free away from the origin. We will compute the topological Ktheory of the real and complex group C ∗algebra of Γ and show that Γ satisfies the unstable GromovLawsonRosenberg Conjecture. On the wa ..."
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Cited by 6 (4 self)
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Let Γ be a semidirect product of the form Z n ⋊ρ Z/p where p is primeand the Zpaction ρ on Z n is free away from the origin. We will compute the topological Ktheory of the real and complex group C ∗algebra of Γ and show that Γ satisfies the unstable GromovLawsonRosenberg Conjecture. On the way we will analyze the (co)homology and the topological Ktheory of the classifying spaces BΓ and BΓ. The latter is the quotient of the induced Z/paction on the torus T n.
KTHEORY FOR RING C*ALGEBRAS – THE CASE OF NUMBER FIELDS WITH HIGHER ROOTS OF UNITY
, 1201
"... Abstract. We compute Ktheory for ring C*algebras in the case of higher roots of unity and thereby completely determine the Ktheory for ring C*algebras attached to rings of integers in arbitrary number fields. 1. ..."
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Abstract. We compute Ktheory for ring C*algebras in the case of higher roots of unity and thereby completely determine the Ktheory for ring C*algebras attached to rings of integers in arbitrary number fields. 1.
TOPOLOGICAL KTHEORY OF THE GROUP C∗ALGEBRA OF A SEMIDIRECT PRODUCT Z n ⋊Z/m FOR A FREE CONJUGATION ACTION
, 2011
"... We compute the topological Ktheory of the group C ∗algebra C ∗ r (Γ) for a group extension 1 → Zn → Γ → Z/m → 1 provided that the conjugation action of Z/m on Z n is free outside the origin. ..."
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Cited by 2 (0 self)
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We compute the topological Ktheory of the group C ∗algebra C ∗ r (Γ) for a group extension 1 → Zn → Γ → Z/m → 1 provided that the conjugation action of Z/m on Z n is free outside the origin.
NONCOMMUTATIVE GEOMETRY AND ARITHMETIC
"... Abstract. This is an overview of recent results aimed at developing a geometry of noncommutative tori with real multiplication, with the purpose of providing a parallel, for real quadratic fields, of the classical theory of elliptic curves with complex multiplication for imaginary quadratic fields. ..."
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Abstract. This is an overview of recent results aimed at developing a geometry of noncommutative tori with real multiplication, with the purpose of providing a parallel, for real quadratic fields, of the classical theory of elliptic curves with complex multiplication for imaginary quadratic fields. This talk concentrates on two main aspects: the relation of Stark numbers to the geometry of noncommutative tori with real multiplication, and the shadows of modular forms on the noncommutative boundary of modular curves, that is, the moduli space of noncommutative tori. 1.