Results 1 to 10 of about 461,348 (110)

Modular Theory, Non-Commutative Geometry and Quantum Gravity [PDF]

, 2010
This paper contains the first written exposition of some ideas (announced in a previous survey) on an approach to quantum gravity based on Tomita-Takesaki modular theory and A.
Bertozzini, Paolo, Conti, Roberto, Lewkeeratiyutkul, Wicharn   +2 more
core   +4 more sources

Free joinings of C*-dynamical systems [PDF]

, 2008
Joinings of C*-dynamical systems are defined in terms of free products of C*-algebras, as an analogue of joinings of classical dynamical systems. We then consider disjointness in this context, in particular for ergodic versus identity systems.
Abadie, Accardi, Andries, Andries, Avitzour, Avitzour, Benatti, Bratteli, Ching, de la Rue, del Junco, Duvenhage, Duvenhage, Fidaleo, Fidaleo, Furstenberg, Glasner, Mukhamedov, Narnhofer, Rocco Duvenhage, Rudolph, Ryzhikov, Sauvageot, Voiculescu, Voiculescu, Voiculescu   +25 more
core   +3 more sources

Compact quantum metric spaces and ergodic actions of compact quantum groups [PDF]

, 2008
We show that for any co-amenable compact quantum group A=C(G) there exists a unique compact Hausdorff topology on the set EA of isomorphism classes of ergodic actions of G such that the following holds: for any continuous field of ergodic actions of G ...
Li, Hanfeng
core   +3 more sources

Orbit Representations from Linear mod 1 Transformations [PDF]

, 2012
We show that every point $x_0\in [0,1]$ carries a representation of a $C^*$-algebra that encodes the orbit structure of the linear mod 1 interval map $f_{\beta,\alpha}(x)=\beta x +\alpha$.
Martins, Nuno, Pinto, Paulo R., Ramos, Carlos Correia   +2 more
core   +4 more sources

Subproduct systems and Cartesian systems; new results on factorial languages and their relations with other areas [PDF]

, 2020
We point out that a sequence of natural numbers is the dimension sequence of a subproduct system if and only if it is the cardinality sequence of a word system (or factorial language).
Gerhold, Malte, Skeide, Michael
core   +3 more sources

The Cuntz semigroup and stability of close C*-algebras [PDF]

, 2013
We prove that separable C*-algebras which are completely close in a natural uniform sense have isomorphic Cuntz semigroups, continuing a line of research developed by Kadison - Kastler, Christensen, and Khoshkam.
Perera, Francesc, Toms, Andrew, White, Stuart, Winter, Wilhelm   +3 more
core   +2 more sources

Quasitriangular operator algebras [PDF]

arXiv, 2022
We give characterizations of quasitriangular operator algebras along the line of Voiculescu's characterization of quasidiagonal $C^*$-algebras.
arxiv  

Classification of non-Kac compact quantum groups of SU(n) type [PDF]

, 2015
We classify up to isomorphism all non-Kac compact quantum groups with the same fusion rules and dimension function as $SU(n)$. For this we first prove, using categorical Poisson boundary, the following general result.
Neshveyev, Sergey, Yamashita, Makoto
core   +2 more sources

The problem of completeness for Gromov-Hausdorff metrics on C*-algebras [PDF]

, 2005
It is proved that the family of equivalence classes of Lip-normed C*-algebras introduced by M. Rieffel, up to isomorphisms preserving the Lip-seminorm, is not complete w.r.t. the matricial quantum Gromov-Hausdorff distance introduced by D. Kerr.
Guido, Daniele, Isola, Tommaso
core   +3 more sources

A $P$-Adic Spectral Triple [PDF]

, 2014
We construct a spectral triple for the C$^*$-algebra of continuous functions on the space of $p$-adic integers by using a rooted tree obtained from coarse-grained approximation of the space, and the forward derivative on the tree. Additionally, we verify
Klimek, Slawomir, McBride, Matt, Rathnayake, Sumedha   +2 more
core   +1 more source