Introduction to the classification of operator algebras

2016 ◽  
Vol 46 (12) ◽  
pp. 1773-1790
Author(s):  
LIN HuaXin
Keyword(s):  
Operator Algebras

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

Classification of irreducible weak modules over Virasoro vertex operator algebras

2019 ◽  
Vol 30 (11) ◽  
pp. 1950054
Author(s):  
Guobo Chen ◽  
Dejia Cheng ◽  
Jianzhi Han ◽  
Yucai Su
Keyword(s):  
Vertex Operator ◽  
Operator Algebra ◽  
Vertex Operator Algebra ◽  
Operator Algebras ◽  
Vertex Operator Algebras ◽  
Positive Integers ◽  
Coprime Positive Integers

The classification of irreducible weak modules over the Virasoro vertex operator algebra [Formula: see text] is obtained in this paper. As one of the main results, we also classify all irreducible weak modules over the simple Virasoro vertex operator algebras [Formula: see text] for [Formula: see text] [Formula: see text], where [Formula: see text] are coprime positive integers.

scholarly journals Classification of extremal vertex operator algebras with two simple modules

2020 ◽  
Vol 61 (5) ◽  
pp. 052302
Author(s):  
J. Connor Grady ◽  
Ching Hung Lam ◽  
James E. Tener ◽  
Hiroshi Yamauchi
Keyword(s):  
Vertex Operator ◽  
Operator Algebras ◽  
Vertex Operator Algebras ◽  
Simple Modules

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.

Classification of domains of operator algebras

1976 ◽  
Vol 9 (2) ◽  
pp. 205-217 ◽  
Author(s):  
G. Lassner ◽  
W. Timmermann
Keyword(s):  
Operator Algebras
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