English
Related papers

Related papers: Tensor product of Vertex operator algebras

200 papers

By a pointed vertex operator algebra (VOA) we mean one whose modules are all simple currents (i.e. invertible), e.g. lattice VOAs. This paper systematically explores the interplay between their orbifolds and tensor category theory. We begin…

Quantum Algebra · Mathematics 2024-10-02 Terry Gannon , Andrew Riesen

We introduce the main concepts and announce the main results in a theory of tensor products for module categories for a vertex operator algebra. This theory is being developed in a series of papers including hep-th 9309076 and hep-th…

High Energy Physics - Theory · Physics 2008-02-03 Yi-Zhi Huang , James Lepowsky

We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ''conformal vertex algebra'' or even more generally,…

Quantum Algebra · Mathematics 2008-07-07 Yi-Zhi Huang , James Lepowsky , Lin Zhang

We consider C-graded vertex algebras, which are vertex algebras V with a C-grading such that V is an admissible V-module generated by 'lowest weight vectors'. We show that such vertex algebras have a 'good' representation theory in the…

Quantum Algebra · Mathematics 2015-06-16 Rob Laber , Geoffrey Mason

We incorporate a category of certain modules for an affine Lie algebra, of a certain fixed non-positive-integral level, considered by Kazhdan and Lusztig, into the representation theory of vertex operator algebras, by using the logarithmic…

Quantum Algebra · Mathematics 2007-05-23 Lin Zhang

We show that the representation theory for the toroidal extended affine Lie algebras is controlled by a vertex operator algebra which is a tensor product of four VOAs: a sub-VOA of the hyperbolic lattice VOA, two affine VOAs and a Virasoro…

Representation Theory · Mathematics 2009-10-13 Yuly Billig

An explicit vertex operator algebra construction is given of a class of irreducible modules for toroidal Lie algebras.

Quantum Algebra · Mathematics 2007-05-23 S. Berman , Y. Billig , J. Szmigielski

In this paper we discuss the structure of the tensor product V'_{\alpha,\beta}\otimes L(c,h) of irreducible module from intermediate series and irreducible highest weight module over the Virasoro algebra. We generalize Zhang's…

Representation Theory · Mathematics 2013-08-12 Gordan Radobolja

The comultiplication formula for fusion products of untwisted representations of the chiral algebra is generalised to include arbitrary twisted representations. We show that the formulae define a tensor product with suitable properties, and…

High Energy Physics - Theory · Physics 2009-10-30 M. R. Gaberdiel

We found a necessary and sufficient condition for the existence of the tensor product of modules over a vertex algebra. We defined the notion of vertex bilinear map and we provide two algebraic construction of the tensor product, where one…

Quantum Algebra · Mathematics 2016-09-27 Jose I. Liberati

We construct vertex operator representations for the full (N+1)-toroidal Lie algebra g. We associate with g a toroidal vertex operator algebra, which is a tensor product of an affine VOA, a sub-VOA of a hyperbolic lattice VOA, affine sl(N)…

Representation Theory · Mathematics 2007-05-23 Yuly Billig

We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ``conformal vertex algebra'' or even more generally,…

Quantum Algebra · Mathematics 2007-05-23 Yi-Zhi Huang , James Lepowsky , Lin Zhang

In this paper we study the representation theory for certain ``half lattice vertex algebras.'' In particular we construct a large class of irreducible modules for these vertex algebras. We also discuss how the representation theory of these…

Quantum Algebra · Mathematics 2007-05-23 Stephen Berman , Chongying Dong , Shaobin Tan

We give a new, construction-free proof of the associativity of tensor product for modules for rational vertex operator algebras under certain convergence conditions.

q-alg · Mathematics 2008-02-03 Chongying Dong , Haisheng Li , Geoffrey Mason

We describe Zhu recursion for a vertex operator algebra (VOA) and its modules on a genus $g$ Riemann surface in the Schottky uniformisation. We show that $n$-point (intertwiner) correlation functions are written as linear combinations of…

Quantum Algebra · Mathematics 2024-10-30 Michael P. Tuite , Michael Welby

We prove a theorem about the derivation algebra of the tensor product of two algebras. As an application, we determine the derivation algebra of the fixed point algebra of the tensor product of two algebras, with respect to the tensor…

Quantum Algebra · Mathematics 2007-05-23 Saeid Azam

This is an expository article invited for the ``Commentary'' section of PNAS in connection with Y.-Z. Huang's article, ``Vertex operator algebras, the Verlinde conjecture, and modular tensor categories,'' appearing in the same issue of…

Quantum Algebra · Mathematics 2009-11-11 James Lepowsky

Let $N_{k} (\g)$ be a vertex operator algebra (VOA) associated to the generalized Verma module for affine Lie algebra of type $A_{\ell -1} ^{(1)}$ or $C_{\ell} ^{(1)}$. We construct a family of ideals $J_{m,n} (\g)$ in $N_{k} (\g)$, and a…

Quantum Algebra · Mathematics 2007-05-23 Drazen Adamovic

In this paper, we use the twisted regular representation theory of vertex operator algebras to construct bimodules over twisted Zhu algebras, extending Haisheng Li's work in untwisted scenarios. Moreover, a conjecture of Dong and Jiang on…

Quantum Algebra · Mathematics 2025-05-23 Yiyi Zhu

We study the general twisted intertwining operators (intertwining operators among twisted modules) for a vertex operator algebra $V$. We give the skew-symmetry and contragredient isomorphisms between spaces of twisted intertwining operators…

Quantum Algebra · Mathematics 2025-07-08 Jishen Du , Yi-Zhi Huang