Type classification of extreme quantized characters

2019 ◽  
Vol 41 (2) ◽  
pp. 593-605
Author(s):  
RYOSUKE SATO
Keyword(s):  
Dynamical Systems ◽  
Quantum Groups ◽  
Asymptotic Representation ◽  
Operator Algebras ◽  
Complete Solution ◽  
Unitary Groups ◽  
Inductive System ◽  
Von Neumann ◽  
Type Classification

The notion of quantized characters was introduced in our previous paper as a natural quantization of characters in the context of asymptotic representation theory for quantum groups. As in the case of ordinary groups, the representation associated with any extreme quantized character generates a von Neumann factor. From the viewpoint of operator algebras (and measurable dynamical systems), it is natural to ask what is the Murray–von Neumann–Connes type of the resulting factor. In this paper, we give a complete solution to this question when the inductive system is of quantum unitary groups $U_{q}(N)$.

scholarly journals Classification of irreversible and reversible Pimsner operator algebras

2020 ◽  
Vol 156 (12) ◽  
pp. 2510-2535
Author(s):  
Adam Dor-On ◽  
Søren Eilers ◽  
Shirly Geffen
Keyword(s):  
Algebraic Structure ◽  
Operator Algebras ◽  
Directed Graphs ◽  
Adjoint Operator ◽  
Neumann Operator ◽  
Von Neumann ◽  
Shed Light

AbstractSince their inception in the 1930s by von Neumann, operator algebras have been used to shed light on many mathematical theories. Classification results for self-adjoint and non-self-adjoint operator algebras manifest this approach, but a clear connection between the two has been sought since their emergence in the late 1960s. We connect these seemingly separate types of results by uncovering a hierarchy of classification for non-self-adjoint operator algebras and $C^{*}$-algebras with additional $C^{*}$-algebraic structure. Our approach naturally applies to algebras arising from $C^{*}$-correspondences to resolve self-adjoint and non-self-adjoint isomorphism problems in the literature. We apply our strategy to completely elucidate this newly found hierarchy for operator algebras arising from directed graphs.

Factoriality and Type Classification of k-Graph von Neumann Algebras

2016 ◽  
Vol 60 (2) ◽  
pp. 499-518 ◽  
Author(s):  
Dilian Yang
Keyword(s):  
Fixed Point ◽  
Von Neumann Algebra ◽  
Von Neumann Algebras ◽  
Von Neumann ◽  
Single Vertex ◽  
Tracial State ◽  
Graph Von Neumann Algebras ◽  
Fixed Point Algebra ◽  
Type Classification

AbstractLet be a single vertex k-graph and let be the von Neumann algebra induced from the Gelfand–Naimark–Segal (GNS) representation of a distinguished state ω of its k-graph C*-algebra . In this paper we prove the factoriality of , and furthermore determine its type when either has the little pullback property, or the intrinsic group of has rank 0. The key step to achieving this is to show that the fixed-point algebra of the modular action corresponding to ω has a unique tracial state.

scholarly journals Integrable and Chaotic Systems Associated with Fractal Groups

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 237
Author(s):  
Rostislav Grigorchuk ◽  
Supun Samarakoon
Keyword(s):  
Operator Algebras ◽  
Probabilistic Approach ◽  
Schur Complement ◽  
Automata Theory ◽  
Random Schrödinger Operators ◽  
Rational Maps ◽  
Holomorphic Dynamics ◽  
Von Neumann ◽  
Intermediate Growth ◽  
Quasi Crystals

Fractal groups (also called self-similar groups) is the class of groups discovered by the first author in the 1980s with the purpose of solving some famous problems in mathematics, including the question of raising to von Neumann about non-elementary amenability (in the association with studies around the Banach-Tarski Paradox) and John Milnor’s question on the existence of groups of intermediate growth between polynomial and exponential. Fractal groups arise in various fields of mathematics, including the theory of random walks, holomorphic dynamics, automata theory, operator algebras, etc. They have relations to the theory of chaos, quasi-crystals, fractals, and random Schrödinger operators. One important development is the relation of fractal groups to multi-dimensional dynamics, the theory of joint spectrum of pencil of operators, and the spectral theory of Laplace operator on graphs. This paper gives a quick access to these topics, provides calculation and analysis of multi-dimensional rational maps arising via the Schur complement in some important examples, including the first group of intermediate growth and its overgroup, contains a discussion of the dichotomy “integrable-chaotic” in the considered model, and suggests a possible probabilistic approach to studying the discussed problems.

scholarly journals Geometric and Topological Bases of a New Classification of Wood Vascular Tissues Part 1: Shape and Arrangement Classifications of Vessels

2021 ◽  
Vol 13 (14) ◽  
pp. 7545
Author(s):  
Nikolai Bardarov ◽  
Vladislav Todorov ◽  
Nicole Christoff
Keyword(s):  
Computer Vision ◽  
Detailed Analysis ◽  
Tree Species ◽  
Complete Solution ◽  
New Classification ◽  
Topological Characteristics ◽  
Definition Of ◽  
Wood Science ◽  
Quantitative Indicators

The need to identify wood by its anatomical features requires a detailed analysis of all the elements that make it up. This is a significant problem of structural wood science, the most general and complete solution of which is yet to be sought. In recent years, increasing attention has been paid to the use of computer vision methods to automate processes such as the detection, identification, and classification of different tissues and different tree species. The more successful use of these methods in wood anatomy requires a more precise and comprehensive definition of the anatomical elements, according to their geometric and topological characteristics. In this article, we conduct a detailed analysis of the limits of variation of the location and grouping of vessels in the observed microscopic samples. The present development offers criteria and quantitative indicators for defining the terms shape, location, and group of wood tissues. It is proposed to differentiate the quantitative indicators of the vessels depending on their geometric and topological characteristics. Thus, with the help of computer vision technics, it will be possible to establish topological characteristics of wood vessels, the extraction of which would be used to develop an algorithm for the automatic classification of tree species.

Automatic Grain Type Classification of Snow Micro Penetrometer Signals With Random Forests

2013 ◽  
Vol 51 (6) ◽  
pp. 3328-3335 ◽  
Author(s):  
Scott Havens ◽  
Hans-Peter Marshall ◽  
Christine Pielmeier ◽  
Kelly Elder
Keyword(s):  
Random Forests ◽  
Type Classification

James Cummings and Ernest Schimmerling, editors. Lecture Note Series of the London Mathematical Society, vol. 406. Cambridge University Press, New York, xi + 419 pp. - Paul B. Larson, Peter Lumsdaine, and Yimu Yin. An introduction to Pmax forcing. pp. 5–23. - Simon Thomas and Scott Schneider. Countable Borel equivalence relations. pp. 25–62. - Ilijas Farah and Eric Wofsey. Set theory and operator algebras. pp. 63–119. - Justin Moore and David Milovich. A tutorial on set mapping reflection. pp. 121–144. - Vladimir G. Pestov and Aleksandra Kwiatkowska. An introduction to hyperlinear and sofic groups. pp. 145–185. - Itay Neeman and Spencer Unger. Aronszajn trees and the SCH. pp. 187–206. - Todd Eisworth, Justin Tatch Moore, and David Milovich. Iterated forcing and the Continuum Hypothesis. pp. 207–244. - Moti Gitik and Spencer Unger. Short extender forcing. pp. 245–263. - Alexander S. Kechris and Robin D. Tucker-Drob. The complexity of classification problems in ergodic theory. pp. 265–299. - Menachem Magidor and Chris Lambie-Hanson. On the strengths and weaknesses of weak squares. pp. 301–330. - Boban Veličković and Giorgio Venturi. Proper forcing remastered. pp. 331–362. - Asger ToÖrnquist and Martino Lupini. Set theory and von Neumann algebras. pp. 363–396. - W. Hugh Woodin, Jacob Davis, and Daniel RodrÍguez. The HOD dichotomy. pp. 397–419.

2014 ◽  
Vol 20 (1) ◽  
pp. 94-97
Author(s):  
Natasha Dobrinen
Keyword(s):  
New York ◽  
Set Theory ◽  
Von Neumann Algebras ◽  
Operator Algebras ◽  
Continuum Hypothesis ◽  
London Mathematical Society ◽  
Equivalence Relations ◽  
Classification Problems ◽  
Von Neumann ◽  
Borel Equivalence Relations

scholarly journals Construction and classification of holomorphic vertex operator algebras

2020 ◽  
Vol 2020 (759) ◽  
pp. 61-99 ◽  
Author(s):  
Jethro van Ekeren ◽  
Sven Möller ◽  
Nils R. Scheithauer
Keyword(s):  
Vertex Operator ◽  
Operator Algebras ◽  
Central Charge ◽  
Field Theories ◽  
Vertex Operator Algebras ◽  
Conformal Field Theories ◽  
Cyclic Groups ◽  
Conformal Field

AbstractWe develop an orbifold theory for finite, cyclic groups acting on holomorphic vertex operator algebras. Then we show that Schellekens’ classification of {V_{1}}-structures of meromorphic conformal field theories of central charge 24 is a theorem on vertex operator algebras. Finally, we use these results to construct some new holomorphic vertex operator algebras of central charge 24 as lattice orbifolds.

scholarly journals Classification of central extensions of Lax operator algebras

2008 ◽  
Author(s):  
Martin Schlichenmaier ◽  
Piotr Kielanowski ◽  
Anatol Odzijewicz ◽  
Martin Schlichenmaier ◽  
Theodore Voronov
Keyword(s):  
Operator Algebras ◽  
Central Extensions ◽  
Lax Operator
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