Related papers: On Square Roots of the Haar State on Compact Quant…
Convolution semigroups of states on a quantum group form the natural noncommutative analogue of convolution semigroups of probability measures on a locally compact group. Here we initiate a theory of weakly continuous convolution semigroups…
This thesis is devoted to the study of Lie bialgebra and Hopf algebra structures related to certain versions of non-commutative geometry constructed on infinite-dimensional Lie algebras that arise in the context of asymptotic symmetries of…
We study the explicit construction of the Haar measure on the compact $p$-adic rotation group $\textrm{SO}(3)_p$ by nautical (Cardano) parametrization. Exploiting its topological group isomorphism with…
Irreducible representations of quantum groups $SL_q(2)$ (in Woronowicz' approach) were classified in J.Wang, B.Parshall, Memoirs AMS 439 in the~case of $q$ being an~odd root of unity. Here we find the~irreducible representations for all…
Let X be a compact Abelian group. In the article we obtain a characterization of shifts of Haar distributions on compact open subgroups of the group X by the symmetry of the conditional distribution of one linear form of independent random…
In this paper, we give an alternative approach to the theory of locally compact quantum groups, as developed by Kustermans and Vaes. We develop the theory completely within the von Neumann algebra framework. At various points, we also do…
To any complex Hadamard matrix we associate a quantum permutation group. The correspondence is not one-to-one, but the quantum group encapsulates a number of subtle properties of the matrix. We investigate various aspects of the…
Conformal inclusions of chiral conformal field theories, or more generally inclusions of quantum field theories, are described in the von Neumann algebraic setting by nets of subfactors, possibly with infinite Jones index if one takes…
The subject of this paper is the study of convolution semigroups of states on a locally compact quantum group, generalising classical families of distributions of a L\'{e}vy process on a locally compact group. In particular a definitive…
In this paper we complete in several aspects the picture of locally compact quantum groups. First of all we give a definition of a locally compact quantum group in the von Neumann algebraic setting and show how to deduce from it a…
In this paper, we investigate the evaluation problem of the Haar state on the quantum group $O(U_q(n))$ ($n\ge 3$) which is a $q$-deformation of the Haar measure on the Lie group $U(n)$. The relation between the Haar state values of…
We give local upper and lower bounds for the eigenvalues of the modular operator associated to an ergodic action of a compact quantum group on a unital C*-algebra. They involve the modular theory of the quantum group and the growth rate of…
We give a necessary and sufficient condition on a compact semitopological quantum semigroup which turns it into a compact quantum group. In particular, we obtain a generalisation of Ellis's joint continuity theorem. We also investigate the…
We introduce the coherent algebra of a compact metric measure space by analogy with the corresponding concept for a finite graph. As an application we show that upon topologizing the collection of isomorphism classes of compact metric…
We consider possible non-signaling composites of probabilistic models based on euclidean Jordan algebras. Subject to some reasonable constraints, we show that no such composite exists having the exceptional Jordan algebra as a direct…
According to Haar's Theorem, every compact group $G$ admits a unique (regular, right and) left-invariant Borel probability measure $\mu_G$. Let the Haar integral (of $G$) denote the functional $\int_G:\mathcal{C}(G)\ni f\mapsto \int…
We consider a twisted version of quantum groups corepresentations. This generalization amounts to include in the theory the case where quantum space coordinates and its endomorphism matrix entries belong to a non-commutative quadratic…
Quantum groupoids are a joint generalization of groupoids and quantum groups. We propose a definition of a compact quantum groupoid that is based on the theory of C*-algebras and Hilbert bimodules. The essential point is that whenever one…
We study states on the universal noncommutative *-algebra generated by the coefficients of a unitary matrix, or equivalently states on the unitary dual group. Its structure of dual group in the sense of Voiculescu allows to define five…
This article provides a concise introduction to the theory of Haar measures on locally compact Hausdorff groups. We cover the necessary preliminaries on topological groups and measure theory, the Haar correspondence, unimodularity and Haar…