Sergey Neshveyev
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Crystallization of $$\hbox {C}^*$$-Algebras Open
Given a $$\hbox {C}^*$$ -algebra A with an almost periodic time evolution $$\sigma $$ , we define a new $$\hbox {C}^*$$ -algebra $$A_c$$ , which we call the crystal of $$(A,\sigma )$$ , that represents the zero temperature limit of $$(A, \…
The ideal structure of C*-algebras of etale groupoids with isotropy groups of local polynomial growth Open
Given an amenable second countable Hausdorff locally compact étale groupoid $\mathcal G$ such that each isotropy group $\mathcal G^x_x$ has local polynomial growth, we give a description of $\operatorname{Prim} C^*(\mathcal G)$ as a topolo…
The primitive spectrum of C*-algebras of etale groupoids with abelian isotropy Open
Given a Hausdorff locally compact étale groupoid $\mathcal G$, we describe as a topological space the part of the primitive spectrum of $C^*(\mathcal G)$ obtained by inducing one-dimensional representations of amenable isotropy groups of $…
Quantization of locally compact groups associated with essentially bijective 1-cocycles Open
Given an extension [Formula: see text] of locally compact groups, with [Formula: see text] abelian, and a compatible essentially bijective [Formula: see text]-cocycle [Formula: see text], we define a dual unitary [Formula: see text]-cocycl…
Cocycle Twisting of Semidirect Products and Transmutation Open
We apply Majid’s transmutation procedure to Hopf algebra maps $H \to {{\mathbb {C}}}[T]$, where $T$ is a compact abelian group, and explain how this construction gives rise to braided Hopf algebras over quotients of $T$ by subgroups that a…
Crystallization of C*-algebras Open
Given a C$^*$-algebra $A$ with an almost periodic time evolution $σ$, we define a new C$^*$-algebra $A_c$, which we call the crystal of $(A,σ)$, that represents the zero temperature limit of $(A, σ)$. We prove that there is a one-to-one co…
KK-duality for the Cuntz-Pimsner algebras of Temperley-Lieb subproduct systems Open
We prove that the Cuntz-Pimsner algebra of every Temperley-Lieb subproduct system is KK-self-dual. We show also that every such Cuntz-Pimsner algebra has a canonical KMS-state, which we use to construct a Fredholm module representative for…
Quantization of locally compact groups associated with essentially bijective $1$-cocycles Open
Given an extension $0\to V\to G\to Q\to1$ of locally compact groups, with $V$ abelian, and a compatible essentially bijective $1$-cocycle $η\colon Q\to\hat V$, we define a dual unitary $2$-cocycle on $G$ and show that the associated deform…
Subproduct systems with quantum group symmetry Open
We introduce a class of subproduct systems of finite dimensional Hilbert spaces whose fibers are defined by the Jones–Wenzl projections in Temperley–Lieb algebras. The quantum symmetries of a subclass of these systems are the free orthogon…
Isotropy fibers of ideals in groupoid C$^{*}$-algebras Open
Given a locally compact étale groupoid and an ideal $I$ in its groupoid C$^*$-algebra, we show that $I$ defines a family of ideals in group C$^*$-algebras of the isotropy groups and then study to which extent $I$ is determined by this fami…
Cocycle twisting of semidirect products and transmutation Open
We apply Majid's transmutation procedure to Hopf algebra maps $H \to \mathbb C[T]$, where $T$ is a compact abelian group, and explain how this construction gives rise to braided Hopf algebras over quotients of $T$ by subgroups that are coc…
Comparison of quantizations of symmetric spaces: cyclotomic Knizhnik–Zamolodchikov equations and Letzter–Kolb coideals Open
We establish an equivalence between two approaches to quantization of irreducible symmetric spaces of compact type within the framework of quasi-coactions, one based on the Enriquez–Etingof cyclotomic Knizhnik–Zamolodchikov (KZ) equations …
Subproduct systems with quantum group symmetry. II Open
We complete our analysis of the Temperley-Lieb subproduct systems, which define quantum analogues of Arveson's $2$-shift, by extending the main results of the previous paper to the general parameter case. Specifically, we show that the ass…
Non-Hausdorff etale groupoids and C*-algebras of left cancellative monoids Open
We study the question whether the representations defined by a dense subset of the unit space of a locally compact étale groupoid are enough to determine the reduced norm on the groupoid C$^*$-algebra. We present sufficient conditions for …
(Non)exotic completions of the group algebras of isotropy groups Open
Motivated by the problem of characterizing KMS states on the reduced C∗-algebras of étale groupoids, we show that the reduced norm on these algebras induces a C∗-norm on the group algebras of the isotropy groups. This C∗-norm coincides wit…
The groupoid approach to equilibrium states on right LCM semigroup C∗$^*$‐algebras Open
Given a right LCM semigroup $S$ and a homomorphism $N\colon S\to[1,+\infty)$, we use the groupoid approach to study the KMS$_β$-states on $C^*(S)$ with respect to the dynamics induced by $N$. We establish necessary and sufficient condition…
Subproduct systems with quantum group symmetry Open
We introduce a class of subproduct systems of finite dimensional Hilbert spaces whose fibers are defined by the Jones-Wenzl projections in Temperley-Lieb algebras. The quantum symmetries of a subclass of these systems are the free orthogon…
(Non)exotic Completions of the Group Algebras of Isotropy Groups Open
Motivated by the problem of characterizing KMS states on the reduced C$^*$-algebras of étale groupoids, we show that the reduced norm on these algebras induces a C$^*$-norm on the group algebras of the isotropy groups. This C$^*$-norm coin…
Noncommutative Poisson boundaries and Furstenberg-Hamana boundaries of Drinfeld doubles Open
We clarify the relation between noncommutative Poisson boundaries and Furstenberg-Hamana boundaries of quantum groups. Specifically, given a compact quantum group $G$, we show that in many cases where the Poisson boundary of the dual discr…
Noncommutative Borsuk–Ulam-type conjectures revisited Open
Let H be the C*-algebra of a non-trivial compact quantum group acting freely on a unital C*-algebra A . It was recently conjectured that there does not exist an equivariant *-homomorphism from A (type-I case) or H (type-II case) to the equ…
Quantization of subgroups of the affine group Open
Consider a locally compact group such that V is abelian and the action of Q on the dual abelian group has a free orbit of full measure. We show that such a group G can be quantized in three equivalent ways:\n(1)\nby reflecting across the G…
Noncommutative Borsuk–Ulam-type conjectures revisited Open
Let H be the C*-algebra of a non-trivial compact quantum group acting freely on a unital C*-algebra A . It was recently conjectured that there does not exist an equivariant *-homomorphism from A (type-I case) or H (type-II case) to the equ…
Addendum: On deformations of C∗-algebras by actions of Kählerian Lie groups Open
We show that two approaches to equivariant deformation of C[Formula: see text]-algebras by actions of negatively curved Kählerian Lie groups, one based on oscillatory integrals and the other on quantizations maps defined by dual [Formula: …
Categorically Morita Equivalent Compact Quantum Groups Open
We give a dynamical characterization of categorical Morita equivalence between compact quantum groups. More precisely, by a Tannaka--Krein type duality, a unital C$^*$-algebra endowed with commuting actions of two compact quantum groups co…
Graded twisting of comodule algebras and module categories Open
Continuing our previous work on graded twisting of Hopf algebras and monoidal categories, we introduce a graded twisting construction for equivariant comodule algebras and module categories. As an example we study actions of quantum subgro…
Categorically Morita Equivalent Compact Quantum Groups Open
We give a dynamical characterization of categorical Morita equivalence between compact quantum groups. More precisely, by a Tannaka-Krein type duality, a unital \mathrm{C}^\ast -algebra endowed with commuting actions of two compact quantum…
On deformations of C∗-algebras by actions of Kählerian Lie groups Open
We show that two approaches to equivariant strict deformation quantization of C[Formula: see text]-algebras by actions of negatively curved Kählerian Lie groups, one based on oscillatory integrals and the other on quantizations maps define…
On deformations of C*-algebras by actions of Kahlerian Lie groups Open
We show that two approaches to equivariant strict deformation quantization of C∗-algebras by actions of negatively curved Kählerian Lie groups, one based on oscillatory integrals and the other on quantizations maps defined by dual 2-cocycl…