Related papers: Thoma type results for discrete quantum groups

We show that if $\Gamma = \Gamma_1\times\dotsb\times \Gamma_n$ is a product of $n\geq 2$ non-elementary ICC hyperbolic groups then any discrete group $\Lambda$ which is $W^*$-equivalent to $\Gamma$ decomposes as a $k$-fold direct sum…

A discrete group $\G$ is called rigidly symmetric if the projective tensor product between the convolution algebra $\ell^1(\G)$ and any $C^*$-algebra $\A$ is symmetric. We show that in each topologically graded $C^*$-algebra over a rigidly…

We consider a locally compact Hausdorff groupoid $G$, and twist by a more general locally compact Hausdorff abelian group $\Gamma$ rather than the complex unit circle $\mathbb{T}$. We investigate the construction of $C^*$-algebras in…

We provide a new large class of countable icc groups $\mathcal A$ for which the product rigidity result from [CdSS15] holds: if $\Gamma_1,\dots,\Gamma_n\in\mathcal A$ and $\Lambda$ is any group such that…

Let $G$ be a simple algebraic group over an algebraically closed field $k$. Let $\Gamma$ be a finite group acting on $G$. We classify and compute the local types of $(\Gamma, G)$-bundles on a smooth projective $\Gamma$-curve in terms of the…

Quantum symmetry of a graph $C^{*}$-algebra $C^{*}(\Gamma)$ corresponding to a finite graph $\Gamma$ has been explored by several mathematicians within different categories in the past few years. In this article, we establish that there are…

We prove some stability results for certain classes of C*-algebras. We prove that whenever $A$ is a finite-dimensional C*-algebra, $B$ is a C*-algebra and $\phi\colon A\to B$ is approximately a $^*$-homomorphism then there is an actual…

If a compact quantum group acts faithfully and smoothly (in the sense of Goswami 2009) on a smooth, compact, oriented, connected Riemannian manifold such that the action induces a natural bimodule morphism on the module of sections of the…

Let R be any ring (with 1), \Gamma a group and R\Gamma the corresponding group ring. Let Ext_{R\Gamma}^{*}(M,M) be the cohomology ring associated to the R\Gamma-module M. Let H be a subgroup of finite index of \Gamma. The following is a…

Let $\Gamma_A$ denote the abelian-by-cyclic group associated to an integer-valued, non-singular matrix $A$. We show that if $A$ has no eigenvalues of modulus one, then there are no faithful $C^1$ perturbations of the trivial action $ \iota:…

Let $\Gamma$ be a $T$-ideal of identities of an affine PI-algebra over an algebraically closed field $F$ of characteristic zero. Consider the family $\mathcal{M}_{\Gamma}$ of finite dimensional algebras $\Sigma$ with $Id(\Sigma) = \Gamma$.…

To a graph $\Gamma$ one can associate a C^*-algebra $C^*(\Gamma)$ generated by isometries. Such $C^*$-algebras were studied recently by Crisp and Laca. They are a special case of the Toeplitz C^*-algebras $\mathcal{T}(G, P)$ associated to…

We will introduce a family $\Gamma_\beta, 1 < \beta \in {\mathbb{R}}$ of infinite non-amenable discrete groups as an interpolation of the Higman-Thompson groups $V_n, 1 < n \in {\mathbb{N}}$ by using the topological full groups of the…

A $\Sigma^*$-algebra is a concrete $C^*$-algebra that is sequentially closed in the weak operator topology. We study an appropriate class of $C^*$-modules over $\Sigma^*$-algebras analogous to the class of $W^*$-modules (selfdual…

Let $A$ be a central simple algebra over a number field $K$ with ring of integers $\mathcal{O}_K$, such that either the degree of the algebra $n \ge 3$, or $n=2$ and $A$ is not a totally definite quaternion algebra. Then strong…

We show that if $\Gamma$ is an infinite finitely generated finitely presented sofic group with zero first $L^{2}$ Betti number then the von Neumann algebra $L(\Gamma)$ is strongly $1$-bounded in the sense of Jung. In particular,…

It is well-known that a finitely generated group $\Gamma$ has Kazhdan's property (T) if and only if the Laplacian element $\Delta$ in ${\mathbb R}[\Gamma]$ has a spectral gap. In this paper, we prove that this phenomenon is witnessed in…

Using the formalism of discrete quantum group gauge theory, one can construct the quantum algebras of observables for the Hamiltonian Chern-Simons model. The resulting moduli algebras provide quantizations of the algebra of functions on the…

For a (unital) $C^*$-algebra $\cla$, we construct a $C^*$-algebraic discrete quantum group (DQG) $\clq_{\rm aut}(\cla)$, coacting on $\cla$, which is a quantum generalization of ${\text Aut}(\cla)$ in the framework of discrete quantum…

We define type $\mathfrak{A}$, type $\mathfrak{B}$, type $\mathfrak{C}$ as well as C*-semi-finite C*-algebras. It is shown that a von Neumann algebra is a type $\mathfrak{A}$, type $\mathfrak{B}$, type $\mathfrak{C}$ or C*-semi-finite…