Related papers: Higher l^2-Betti numbers of universal quantum grou…

A standing conjecture in L2-cohomology is that every finite CW-complex X is of L2-determinant class. In this paper, we prove this whenever the fundamental group belongs to a large class of groups containing e.g. all extensions of residually…

Let $n\ge 3$, and let $\mathrm{Out}(W_n)$ be the outer automorphism group of a free Coxeter group $W_n$ of rank $n$. We study the growth of the dimension of the homology groups (with coefficients in any field $\mathbb{K}$) along Farber…

We construct quantization of semisimple conjugacy classes of the exceptional group $G=G_2$ along with and by means of their exact representations in highest weight modules of the quantum group $U_q(\mathfrak{g})$. With every point $t$ of a…

In this paper, we carry out the ``quantum double construction'' of the specific quantum groups we constructed earlier, namely, the ``quantum Heisenberg group algebra'' (A,\Delta) and its dual, the ``quantum Heisenberg group''…

The problem of how to obtain quasi-classical states for quantum groups is examined. A measure of quantum indeterminacy is proposed, which involves expectation values of some natural quantum group operators. It is shown that within any…

Very little is known on the Hilbert series of graded algebras $\mathbb C[x_1,\ldots,x_n]/(g_1,\ldots,g_r)$, $r>n$, $g_i$ generic form of degree $e_i$, in general. One instance when the series is known, is for $n+1$ forms in $n$ variables,…

Finite hamiltonian groups are counted. The sequence of numbers of all groups of order $n$ all whose subgroups are normal and the sequence of numbers of all groups of order less or equal to $n$ all whose subgroups are normal are presented.

We introduce higher-dimensional analogs of Kazhdan projections in matrix algebras over group $C^*$-algebras and Roe algebras. These projections are constructed in the framework of cohomology with coefficients in unitary representations and…

By using the logarithmic approach of the classical kernels for the K2 of number fields, we compute the 2-rank of the wild kernel WK2(F) and the 2-rank of the subgroup of infinite heigh elements in K2(F) in terms of positive class groups for…

In this paper we associate to every reduced C*-algebraic quantum group A a universal C*-algebraic quantum group. We fine tune a proof of Kirchberg to show that every *-representation of a modified L1-space is generated by a unitary…

By encoding a qudit in a harmonic oscillator and investigating the d --> infinity limit, we give an entirely new realization of continuous-variable quantum computation. The generalized Pauli group is generated by number and phase operators…

We construct first examples of infinite finitely generated residually finite torsion groups with positive rank gradient. In particular, these groups are non-amenable. Some applications to problems about cost and $L^2$-Betti numbers are…

We prove that the quantum group inclusion $O_n \subset O_n^*$ is "maximal", where $O_n$ is the usual orthogonal group and $O_n^*$ is the half-liberated orthogonal quantum group, in the sense that there is no intermediate compact quantum…

Motivated by generalizing Szemer\'edi's theorem, we the elements in a discrete quantum group fixing a sequence of finite subsets and prove that the set of these elements is a quantum subgroup. Using this we obtain a version of mean ergodic…

Let $(\bf U, \bf U^\imath)$ be a quantum symmetric pair of Kac-Moody type. The $\imath$quantum groups $\bf U^\imath$ and the universal $\imath$quantum groups $\widetilde{\bf U}^\imath$ can be viewed as a generalization of quantum groups and…

We investigate how one can twist L^2-invariants such as L^2-Betti numbers and L^2-torsion with finite-dimensional representations. As a special case we assign to the universal covering of a finite connected CW-complex X together with an…

We classify discrete quantum subgroups in the quantum double of the $q$-deformation of a compact semisimple Lie group, regarded as the complexification. We also record their classifications in some variants of quantum groups. Along the way,…

We determine which simplicial complexes have the maximum or minimum sum of Betti numbers and sum of bigraded Betti numbers with a given number of vertices in each dimension.

We describe quantum enveloping algebras of symmetric Kac-Moody Lie algebras via a finite field Hall algebra construction involving Z_2-graded complexes of quiver representations.

We prove the solvability and nilpotency of Kac--Paljutkin's finite quantum group and Sekine quantum groups and we classify the solvable series of Kac--Paljutkin's finite quantum group via Cohen--Westreich's Burnside theorem. Some semisimple…