46 citations · 157 across the 23 of their papers we have counts for
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The action of the Thompson group F on infinite trees
Jeong Hee Hong, Wojciech Szymanski
We construct an action of the Thompson group F on a compact space built from pairs of infinite, binary rooted trees. The action arises as an F-equivariant compactification of the a…
Endomorphisms of the Cuntz Algebras and the Thompson Groups
Selçuk Barlak, Jeong Hee Hong, Wojciech Szymanski
We investigate the relationship between endomorphisms of the Cuntz algebra and endomorphisms of the Thompson groups , and represented inside the unitary…
On Conjugacy of MASAs in Graph -Algebras
Tomohiro Hayashi, Jeong Hee Hong, Wojciech Szymanski
For a large class of finite graphs , we show that whenever is a vertex-fixing quasi-free automorphism of the corresponding graph -algebra such that $α({\mathca…
On Endomorphisms of the Cuntz Algebra which Preserve the Canonical UHF-Subalgebra, II
Tomohiro Hayashi, Jeong Hee Hong, Wojciech Szymanski
It was shown recently by Conti, Rørdam and Szymański that there exist endomorphisms of the Cuntz algebra such that …
Pure infiniteness and ideal structure of -algebras associated to Fell bundles
B. K. Kwaśniewski, W. Szymański
We investigate structural properties of the reduced cross-sectional algebra of a Fell bundle over a discrete group . Conditions allowing one t…
On Cohomology for Product Systems
Jeong Hee Hong, Mi Jung Son, Wojciech Szymanski
A cohomology for product systems of Hilbert bimodules is defined via the Ext functor. For the class of product systems corresponding to irreversible algebraic dynamics, relevant re…
Visualizing automorphisms of graph algebras
James Emil Avery, Rune Johansen, Wojciech Szymanski
Graph C*-algebras have been celebrated as C*-algebras that can be seen, because many important properties may be determined by looking at the underlying graph. This paper introduce…
On Conjugacy of MASAs and the Outer Automorphism Group of the Cuntz Algebra
Roberto Conti, Jeong Hee Hong, Wojciech Szymanski
We investigate the structure of the outer automorphism group of the Cuntz algebra and the closely related problem of conjugacy of MASAa in O_n. In particular, we exhibit an uncount…
The Weyl group of the Cuntz algebra
Roberto Conti, Jeong Hee Hong, Wojciech Szymanski
The Weyl group of the Cuntz algebra O_n, with n finite, is investigated. This is (isomorphic to) the group of polynomial automorphisms of O_n, namely those induced by unitaries tha…
Automorphisms of the Cuntz algebras
Roberto Conti, Wojciech Szymanski
We survey recent results on endomorphisms and especially on automorphisms of the Cuntz algebras O_n, with a special emphasis on the structure of the Weyl group. We discuss endomorp…
The Cuntz Algebra Q_N and C*-Algebras of Product Systems
Jeong Hee Hong, Nadia S. Larsen, Wojciech Szymanski
We consider a product system over the multiplicative semigroup N^x of Hilbert bimodules which is implicit in work of S. Yamashita and of the second named author. We prove directly,…
Endomorphisms of the Cuntz Algebras
Roberto Conti, Jeong Hee Hong, Wojciech Szymanski
This mainly expository article is devoted to recent advances in the study of dynamical aspects of the Cuntz algebras O_n, with n finite, via their automorphisms and, more generally…
Endomorphisms of graph algebras
Roberto Conti, Jeong Hee Hong, Wojciech Szymanski
We initiate a systematic investigation of endomorphisms of graph C*-algebras C*(E), extending several known results on endomorphisms of the Cuntz algebras O_n. Most but not all of…
The Restricted Weyl Group of the Cuntz Algebra and Shift Endomorphisms
Roberto Conti, Jeong Hee Hong, Wojciech Szymanski
It is shown that, modulo the automorphisms which fix the canonical diagonal MASA point-wise, the group of those automorphisms of the Cuntz algebra O_n which globally preserve both…
On Invariant MASAs for Endomorphisms of the Cuntz Algebras
Jeong Hee Hong, Adam Skalski, Wojciech Szymanski
The problem of existence of standard (i.e. product-type) invariant MASAs for endomorphisms of the Cuntz algebra O_n is studied. In particular endomorphisms which preserve the canon…
Endomorphisms of O_n which preserve the canonical UHF-subalgebra
Roberto Conti, Mikael Rordam, Wojciech Szymanski
Unital endomorphisms of the Cuntz algebra O_n which preserve the canonical UHF-subalgebra F_n of O_n are investigated. We give examples of such endomorphisms for which the associat…
More localized automorphisms of the Cuntz algebras
Roberto Conti, Jason Kimberley, Wojciech Szymanski
We completely determine the localized automorphisms of the Cuntz algebras corresponding to permutation matrices in for and . This result is obtai…
Computing the Jones index of quadratic permutation endomorphisms of O_2
Roberto Conti, Wojciech Szymanski
We compute the index of the inclusions of type factors arising from endomorphisms of the Cuntz algebra associated to the rank-two permutation matrices.
Labeled Trees and Localized Automorphisms of the Cuntz Algebras
Roberto Conti, Wojciech Szymanski
We initiate a detailed and systematic study of automorphisms of the Cuntz algebras which preserve both the diagonal and the core -subalgebra. A general criterion of inve…
Noncommutative Balls and Mirror Quantum Spheres
Jeong Hee Hong, Wojciech Szymanski
Noncommutative analogues of n-dimensional balls are defined by repeated application of the quantum double suspension to the classical low-dimensional spaces. In the `even-dimension…
The primitive ideal space of the C*-algebras of infinite graphs
Jeong Hee Hong, Wojciech Szymanski
For any countable directed graph E we describe the primitive ideal space of the corresponding generalized Cuntz-Krieger algebra C*(E).
Stable rank of graph algebras. Type I graph algebras and their limits
Klaus Deicke, Jeong Hee Hong, Wojciech Szymanski
For an arbitrary countable directed graph E we show that the only possible values of the stable rank of the associated Cuntz-Krieger algebra C*(E) are 1, 2 or \infty. Explicit crit…
The ideal structure of the C*-algebras of infinite graphs
Teresa Bates, Jeong Hee Hong, Iain Raeburn +1
We classify the gauge-invariant ideals in the C*-algebras of infinite directed graphs, and describe the quotients as graph algebras. We then use these results to identify the gauge…