Generalized Vertex Algebras and Relative Vertex Operators

1993 ◽  
Author(s):  
Chongying Dong ◽  
James Lepowsky
Keyword(s):  
Vertex Algebras ◽  
Vertex Operators

scholarly journals Nonlocal vertex algebras generated by formal vertex operators

2006 ◽  
Vol 11 (3-4) ◽  
pp. 349-397 ◽  
Author(s):  
Haisheng Li
Keyword(s):  
Vertex Algebras ◽  
Vertex Operators

scholarly journals Superconformal vertex algebras in four dimensions

2015 ◽  
Vol 30 (12) ◽  
pp. 1550064
Author(s):  
Dimitar Nedanovski
Keyword(s):  
Vertex Algebras ◽  
Vertex Operators ◽  
Superconformal Symmetry ◽  
Four Dimensions

For vertex algebras with extended superconformal symmetry, in a canonical way, we construct superconformal vertex operators, i.e. fields on the superspace together with a state-field correspondence. This leads to the notion of superconformal vertex algebras (in four dimensions).

scholarly journals N-point locality for vertex operators: Normal ordered products, operator product expansions, twisted vertex algebras

2014 ◽  
Vol 218 (12) ◽  
pp. 2165-2203 ◽  
Author(s):  
Iana I. Anguelova ◽  
Ben Cox ◽  
Elizabeth Jurisich
Keyword(s):  
Vertex Algebras ◽  
Operator Product ◽  
Vertex Operators

scholarly journals Generalized Vertex Algebras Generated by Parafermion-Like Vertex Operators

2001 ◽  
Vol 240 (2) ◽  
pp. 771-807 ◽  
Author(s):  
Yongcun Gao ◽  
Haisheng Li
Keyword(s):  
Vertex Algebras ◽  
Vertex Operators

scholarly journals AXIOMATIC G1-VERTEX ALGEBRAS

2003 ◽  
Vol 05 (02) ◽  
pp. 281-327 ◽  
Author(s):  
HAISHENG LI
Keyword(s):  
Vertex Algebra ◽  
Vertex Algebras ◽  
Vertex Operators ◽  
Vertex Group ◽  
Basic Properties

Inspired by Borcherds' work on "G-vertex algebras," we formulate and study an axiomatic counterpart of Borcherds' notion of G-vertex algebra for the simplest nontrivial elementary vertex group, which we denote by G1. Specifically, we formulate a notion of axiomatic G1-vertex algebra, prove certain basic properties and give certain examples, where the notion of axiomatic G1-vertex algebra is a nonlocal generalization of the notion of vertex algebra. We also show how to construct axiomatic G1-vertex algebras from a set of compatible G1-vertex operators.

scholarly journals HD-QUANTUM VERTEX ALGEBRAS AND BICHARACTERS

2009 ◽  
Vol 11 (06) ◽  
pp. 937-991 ◽  
Author(s):  
IANA I. ANGUELOVA ◽  
MAARTEN J. BERGVELT
Keyword(s):  
Hopf Algebra ◽  
Large Class ◽  
Vertex Algebra ◽  
The State ◽  
Vertex Algebras ◽  
Vertex Operators ◽  
New Class ◽  
Littlewood Polynomials ◽  
Quantum Vertex ◽  
Translation Covariance

We define a new class of quantum vertex algebras, based on the Hopf algebra HD = ℂ[D] of "infinitesimal translations" generated by D. Besides the braiding map describing the obstruction to commutativity of products of vertex operators, HD-quantum vertex algebras have as a main new ingredient a "translation map" that describes the obstruction of vertex operators to satisfying translation covariance. The translation map also appears as obstruction to the state-field correspondence being a homomorphism. We use a bicharacter construction of Borcherds to construct a large class of HD-quantum vertex algebras. One particular example of this construction yields a quantum vertex algebra that contains the quantum vertex operators introduced by Jing in the theory of Hall–Littlewood polynomials.

scholarly journals Polynomial ring representations of endomorphisms of exterior powers

2021 ◽  
Author(s):  
Ommolbanin Behzad ◽  
André Contiero ◽  
Letterio Gatto ◽  
Renato Vidal Martins
Keyword(s):  
Lie Algebra ◽  
Polynomial Ring ◽  
Vertex Operators ◽  
Exterior Power ◽  
Infinite Dimensional ◽  
Symmetric Structure ◽  
Rational Polynomials ◽  
Exterior Powers ◽  
Vertex Representation ◽  
Countably Infinite

AbstractAn explicit description of the ring of the rational polynomials in r indeterminates as a representation of the Lie algebra of the endomorphisms of the k-th exterior power of a countably infinite-dimensional vector space is given. Our description is based on results by Laksov and Throup concerning the symmetric structure of the exterior power of a polynomial ring. Our results are based on approximate versions of the vertex operators occurring in the celebrated bosonic vertex representation, due to Date, Jimbo, Kashiwara and Miwa, of the Lie algebra of all matrices of infinite size, whose entries are all zero but finitely many.

scholarly journals Relating the b ghost and the vertex operators of the pure spinor superstring

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Osvaldo Chandia ◽  
Brenno Carlini Vallilo
Keyword(s):  
Vertex Operator ◽  
Bosonic String ◽  
Vertex Operators ◽  
Pure Spinor ◽  
Double Pole ◽  
Lorenz Gauge

Abstract The OPE between the composite b ghost and the unintegrated vertex operator for massless states of the pure spinor superstring is computed and shown to reproduce the structure of the bosonic string result. The double pole vanishes in the Lorenz gauge and the single pole is shown to be equal to the corresponding integrated vertex operator.

scholarly journals Associating quantum vertex algebras to Lie algebragl∞

2014 ◽  
Vol 399 ◽  
pp. 1086-1106 ◽  
Author(s):  
Cuipo Jiang ◽  
Haisheng Li
Keyword(s):  
Vertex Algebras ◽  
Quantum Vertex
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