scholarly journals Classification of Irreducible Modules for the Vertex Operator Algebra M(1)+

2001 ◽  
Vol 240 (1) ◽  
pp. 289-325 ◽  
Author(s):  
Chongying Dong ◽  
Kiyokazu Nagatomo
Keyword(s):  
Vertex Operator ◽  
Operator Algebra ◽  
Vertex Operator Algebra ◽  
Irreducible Modules

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.

Extension of Vertex Operator Algebra $V_{\widehat{H}_{4}}(\ell,0)$

2014 ◽  
Vol 21 (03) ◽  
pp. 361-380 ◽  
Author(s):  
Cuipo Jiang ◽  
Song Wang
Keyword(s):  
Representation Theory ◽  
Lie Algebra ◽  
Vertex Operator ◽  
Operator Algebra ◽  
Vertex Operator Algebra ◽  
Vertex Algebra ◽  
Irreducible Representations ◽  
Natural Conditions ◽  
Irreducible Modules ◽  
Heisenberg Algebras

We classify the irreducible restricted modules for the affine Nappi-Witten Lie algebra [Formula: see text] with some natural conditions. It turns out that the representation theory of [Formula: see text] is quite different from the theory of representations of Heisenberg algebras. We also study the extension of the vertex operator algebra [Formula: see text] by the even lattice L. We give the structure of the extension [Formula: see text] and its irreducible modules via irreducible representations of [Formula: see text] viewed as a vertex algebra.

scholarly journals Uniqueness results for the moonshine vertex operator algebra

2007 ◽  
Vol 129 (2) ◽  
pp. 583-609 ◽  
Author(s):  
Chongying Dong ◽  
Robert L. Griess ◽  
Ching Hung. Lam
Keyword(s):  
Vertex Operator ◽  
Operator Algebra ◽  
Vertex Operator Algebra ◽  
Uniqueness Results ◽  
Moonshine Vertex Operator Algebra
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