• Corpus ID: 211259207

# Noncommutative Furstenberg boundary

@article{Kalantar2020NoncommutativeFB,
title={Noncommutative Furstenberg boundary},
author={Mehrdad Kalantar and Paweł Kasprzak and Adam G. Skalski and Roland Vergnioux},
journal={arXiv: Operator Algebras},
year={2020}
}
• Published 22 February 2020
• Mathematics
• arXiv: Operator Algebras
We introduce and study the notions of boundary actions and of the Furstenberg boundary of a discrete quantum group. As for classical groups, properties of boundary actions turn out to encode significant properties of the operator algebras associated with the discrete quantum group in question; for example we prove that if the action on the Furstenberg boundary is faithful, the quantum group C*-algebra admits at most one KMS-state for the scaling automorphism group. To obtain these results we…
4 Citations
Existence and Uniqueness of Traces on Discrete Quantum Groups
We ﬁnd quantum group dynamic characterizations of the existence and uniqueness of tracial states on the reduced C ∗ -algebra C r ( b G ) of an arbitrary discrete quantum group G . We prove that C r (
Boundary maps, germs and quasi-regular representations
• Mathematics
• 2022
On Ideals of $L^1$-algebras of Compact Quantum Groups
We develop a notion of a non-commutative hull for a left ideal of the L-algebra of a compact quantum group G. A notion of non-commutative spectral synthesis for compact quantum groups is achieved as
Topological boundaries of connected graphs and Coxeter groups.
We introduce and study certain topological spaces associated with connected rooted graphs. These spaces reflect combinatorial and order theoretic properties of the underlying graph and relate in the

## References

SHOWING 1-10 OF 52 REFERENCES
Non-commutative Poisson Boundaries and Compact Quantum Group Actions
Abstract We discuss some relationships between two different fields, a non-commutative version of the Poisson boundary theory of random walks and the infinite tensor product (ITP) actions of compact
Quantum actions on discrete quantum spaces and a generalization of Clifford’s theory of representations
• Mathematics
Israel Journal of Mathematics
• 2018
To any action of a compact quantum group on a von Neumann algebra which is a direct sum of factors we associate an equivalence relation corresponding to the partition of a space into orbits of the
A Characterization of Right Coideals of Quotient Type and its Application to Classification of Poisson Boundaries
Let $${\mathbb{G}}$$ be a co-amenable compact quantum group. We show that a right coideal of $${\mathbb{G}}$$ is of quotient type if and only if it is the range of a conditional expectation
LOCALLY COMPACT QUANTUM GROUPS IN THE UNIVERSAL SETTING
In this paper we associate to every reduced C*-algebraic quantum group (A, Δ) (as defined in [11]) a universal C*-algebraic quantum group (Au, Δu). We fine tune a proof of Kirchberg to show that
Boundaries of reduced C*-algebras of discrete groups
• Mathematics
• 2014
For a discrete group G, we consider the minimal C*-subalgebra of $\ell^\infty(G)$ that arises as the image of a unital positive G-equivariant projection. This algebra always exists and is unique up
The boundary of universal discrete quantum groups, exactness, and factoriality
• Mathematics
• 2005
We study the C -algebras and von Neumann algebras associated with the universal discrete quantum groups. They give rise to full prime factors and simple exact C -algebras. The main tool in our work
Quantum groups with projection and extensions of locally compact quantum groups
• Mathematics
• 2014
The main result of the paper is the characterization of those locally compact quantum groups with projection, i.e. non-commutative analogs of semidirect products, which are extensions as defined by
Categorical Duality for Yetter-Drinfeld Algebras
• Mathematics
• 2014
We study tensor structures on (RepG)-module cate- gories defined by actions of a compact quantum group G on unital C ∗ -algebras. We show that having a tensor product which defines the module