Introduction to Vertex Operator Algebras and Their Representations

By James Lepowsky, Haisheng Li. 2003

943 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/1b70834babaf156908b6d7c36b3e85d9d17a650c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Kaiming Zhao
2. R. Lu
3. Xiangqian Guo
4. Yi-Zhi Huang
5. C. Dong
6. James Lepowsky
7. Lin Zhang
8. Haisheng Li

In Computational Theory and Mathematics

1. C. Dong
2. Yi-Zhi Huang
3. Haisheng Li
4. R. Lu
5. Kaiming Zhao
6. C. Calinescu
7. Qing Wang
8. Xingjun Lin

Citations in the corpus

• Logarithmic Tensor Category Theory for Generalized Modules for a Conformal Vertex Algebra, I: Introduction and Strongly Graded Algebras and their Generalized Modules (2010, methodology): “Recall from [FLM2], [FHL] or [LL] that the formal delta function is defined as the formal series”
• VERTEX OPERATOR ALGEBRAS AND THE VERLINDE CONJECTURE (2004, background): “t paper have been announced in [H8] and [H9]. See also [Le] for an exposition. We assume that the reader is familiar with the basic theory of vertex operator algebras as presented in [FLM], [FHL] and [LL]. We also assume that the reader has some basic knowledge in the theories of intertwining operat”
• Simple Harish-Chandra modules, intermediate series modules, and Verma modules over the loop-Virasoro algebra (2010, methodology): “The Virasoro algebra theory has been widely used in many physics areas and other mathematical branches, for example, quantum physics [9], conformal field theory [6], higher-dimensional WZW models [11, 12], Kac–Moody algebras [15, 26], vertex algebras [17], and so on.”
• Left-symmetric algebras, or pre-Lie algebras in geometry and physics (2005, neutral): “By definition the product x · y in A satisfies the two conditions x · (y · z)− (x · y) · z = y · (x · z)− (y · x) · z [x, y] = x · y − y · x for all x, y, z ∈ A.”
• Logarithmic extensions of minimal models: characters and modular transformations. (2006, methodology): “Let Lp+,p− be the lattice vertex-operator algebra (see [41, 42, 43 ]) generated by the vertex operators”
• Principal subspaces of higher-level standard sl(3)̂-modules (2006, background): “[20,12,23]) that L(Λ) is graded with respect to a standard action of the Virasoro algebra operator L(0) and that”
• Unitary vertex operator algebras (2013, methodology): “We assume that the readers are familiar with the notion of vertex operator algebra and the basic facts about vertex operator algebra as presented in [FLM], [FHL], [DLM1], [DLM2], [LL] and [Z].”
• W -algebras related to parafermion algebras (2008, background): “Hence U(0) is an A(V )-module, where [v] acts as o(v) on U(0).”
• The Structure of Parafermion Vertex Operator Algebras: General Case (2009, methodology): “7 of [18], there exist nonnegative integers p, q such that”
• Vertex-algebraic structure of the principal subspaces of certain A_1^(1)-modules, II: higher level case (2007, methodology): “As in [2], we shall invoke [18] for material on ideals of vertex (operator) algebras and on vertex-operator algebra and module structure on generalized Verma modules.”
• Vertex algebras and vertex Poisson algebras (2002, methodology): “Then Vλ`(R) is isomorphic to Vĝ(`, 0) as in [23] and to V`(g) as in [15].”
• WHITTAKER MODULES FOR THE VIRASORO ALGEBRA (2008, background): “In his paper, Kostant classified the Whittaker modules of g, demonstrating a strong connection with the center of U(g) among other results on Whittaker modules.”
• Abelianizing Vertex Algebras (2004, background): “for v ∈ V, n∈ Z .I fV is a vertex operator algebra in the sense of [FLM] and [FHL], then D = L(−1), a component of the vertex operator Y( ω, x)= n∈Z L(n)x −n−2 associated to the conformal (or Virasoro) vector ω. (See for example [ LL ] for an exposition of such facts.)”
• A new construction of vertex algebras and quasi-modules for vertex algebras (2004, methodology): “In this section we define certain iota maps, generalizing the iota maps that were introduced in [FHL,FLM] and extended in [LL].”
• Anyon condensation and tensor categories (2013, background): “ no Lagrangian algebra in C. But Ccan still have non-Lagrangian condensable algebras. Many examples of condensable algebras are given by conformal embedding of rational vertex operator algebras (VOA) [LL]. Let Uand V be two rational vertex operator algebras. In particular, it means that the category”