scholarly journals Smash product construction of modular lattice vertex algebras

2021 ◽  
Vol 30 (1) ◽  
pp. 204-220
Author(s):  
Qiang Mu ◽  
Keyword(s):  
Vertex Operator ◽  
Modular Lattice ◽  
Characteristic Zero ◽  
Positive Characteristic ◽  
Operator Algebras ◽  
Positive Definite ◽  
Vertex Operator Algebras ◽  
Vertex Algebras ◽  
Smash Product ◽  
Integral Forms

<abstract><p>Motivated by a work of Li, we study nonlocal vertex algebras and their smash products over fields of positive characteristic. Through smash products, modular vertex algebras associated with positive definite even lattices are reconstructed. This gives a different construction of the modular vertex algebras obtained from integral forms introduced by Dong and Griess in lattice vertex operator algebras over a field of characteristic zero.</p></abstract>

scholarly journals Determinants for integral forms in lattice type vertex operator algebras

2020 ◽  
Vol 558 ◽  
pp. 327-335
Author(s):  
Chongying Dong ◽  
Robert L. Griess
Keyword(s):  
Vertex Operator ◽  
Operator Algebras ◽  
Vertex Operator Algebras ◽  
Lattice Type ◽  
Integral Forms

scholarly journals Integral forms in vertex operator algebras which are invariant under finite groups

2012 ◽  
Vol 365 ◽  
pp. 184-198 ◽  
Author(s):  
Chongying Dong ◽  
Robert L. Griess
Keyword(s):  
Finite Groups ◽  
Vertex Operator ◽  
Operator Algebras ◽  
Vertex Operator Algebras ◽  
Integral Forms

scholarly journals Lattice-integrality of certain group-invariant integral forms in vertex operator algebras

2017 ◽  
Vol 474 ◽  
pp. 505-516 ◽  
Author(s):  
Chongying Dong ◽  
Robert L. Griess
Keyword(s):  
Vertex Operator ◽  
Operator Algebras ◽  
Vertex Operator Algebras ◽  
Group Invariant ◽  
Integral Forms ◽  
Invariant Integral

Hopf actions on vertex operator algebras, II: Smash product

2019 ◽  
Vol 530 ◽  
pp. 402-428
Author(s):  
Hao Wang
Keyword(s):  
Vertex Operator ◽  
Operator Algebras ◽  
Vertex Operator Algebras ◽  
Smash Product

scholarly journals CONSTRUCTING QUANTUM VERTEX ALGEBRAS

2006 ◽  
Vol 17 (04) ◽  
pp. 441-476 ◽  
Author(s):  
HAISHENG LI
Keyword(s):  
Vertex Operator ◽  
Operator Algebra ◽  
Vertex Operator Algebra ◽  
Operator Algebras ◽  
Vertex Algebra ◽  
Vertex Operator Algebras ◽  
Vertex Algebras ◽  
Quantum Vertex

This is a sequel to [23]. In this paper, we focus on the construction of quantum vertex algebras over ℂ, whose notion was formulated in [23] with Etingof and Kazhdan's notion of quantum vertex operator algebra (over ℂ[[h]]) as one of the main motivations. As one of the main steps in constructing quantum vertex algebras, we prove that every countable-dimensional nonlocal (namely, noncommutative) vertex algebra over ℂ, which either is irreducible or has a basis of PBW type, is nondegenerate in the sense of Etingof and Kazhdan. Using this result, we establish the nondegeneracy of better known vertex operator algebras and some newly constructed nonlocal vertex algebras. We construct a family of quantum vertex algebras closely related to Zamolodchikov–Faddeev algebras.

Vertex Operator Algebras and Moonshine: A Survey

2018 ◽  
Author(s):  
Chongying Dong ◽  
Geoffrey Mason
Keyword(s):  
Vertex Operator ◽  
Operator Algebras ◽  
Vertex Operator Algebras

scholarly journals W algebras, cosets and VOAs for 4d $$ \mathcal{N} $$ = 2 SCFTs from M5 branes

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Dan Xie ◽  
Wenbin Yan
Keyword(s):  
Vertex Operator ◽  
Operator Algebras ◽  
Nilpotent Orbit ◽  
Vertex Operator Algebras ◽  
Flavor Symmetries ◽  
Conformal Embedding

Abstract We identify vertex operator algebras (VOAs) of a class of Argyres-Douglas (AD) matters with two types of non-abelian flavor symmetries. They are the W algebras defined using nilpotent orbit with partition [qm, 1s]. Gauging above AD matters, we can find VOAs for more general $$ \mathcal{N} $$ N = 2 SCFTs engineered from 6d (2, 0) theories. For example, the VOA for general (AN − 1, Ak − 1) theory is found as the coset of a collection of above W algebras. Various new interesting properties of 2d VOAs such as level-rank duality, conformal embedding, collapsing levels, coset constructions for known VOAs can be derived from 4d theory.

Z2k-code vertex operator algebras

2021 ◽  
Vol 573 ◽  
pp. 451-475
Author(s):  
Hiromichi Yamada ◽  
Hiroshi Yamauchi
Keyword(s):  
Vertex Operator ◽  
Operator Algebras ◽  
Vertex Operator Algebras
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