# Twisted Heisenberg-Virasoro vertex operator algebra

@article{Guo2016TwistedHV,
title={Twisted Heisenberg-Virasoro vertex operator algebra},
author={Hongyan Guo and Qing Wang},
journal={arXiv: Quantum Algebra},
year={2016}
}
• Published 2016
• Mathematics
• arXiv: Quantum Algebra
In this paper, we study a new kind of vertex operator algebra related to the twisted Heisenberg-Virasoro algebra, which we call the twisted Heisenberg-Virasoro vertex operator algebra, and its modules. Specifically, we present some results concerning the relationship between the restricted module categories of twisted Heisenberg-Virasoro algebras of rank one and rank two and several different kinds of module categories of their corresponding vertex algebras. We also study fully the structures… Expand
7 Citations
Biderivations of the twisted Heisenberg–Virasoro algebra and their applications
• Mathematics
• 2017
ABSTRACT In this paper, the biderivations without the skew-symmetric condition of the twisted Heisenberg–Virasoro algebra are presented. We find some non-inner and non-skew-symmetric biderivations.Expand
The $N=1$ super Heisenberg-Virasoro vertex algebra at level zero
• Mathematics, Physics
• 2020
We study the representation theory of the N=1 super Heisenberg-Virasoro vertex algebra at level zero, which extends the previous work on the Heisenberg-Virasoro vertex algebra arXiv:math/0201314,Expand
Simple restricted modules for the Heisenberg-Virasoro algebra
Abstract We use simple modules over the finite-dimensional solvable Lie algebras to construct many simple restricted modules over the Heisenberg-Virasoro algebra L . These modules contain the highestExpand
Verma modules for rank two Heisenberg-Virasoro algebra
• Mathematics
• Science China Mathematics
• 2019
Let ⪯ be a compatible total order on the additive group ℤ 2 , and L be the rank two Heisenberg-Virasoro algebra. For any c = ( c1, c2, c3, c4 ) ∈ ℂ 4 , we define a ℤ 2 -graded Verma module M ( c , ⪯)Expand
On Harish-Chandra modules of the Lie algebra arising from the $2$-Dimensional Torus
• Mathematics
• 2018
Let A = C[t 1 , t ±1 2 ] be the algebra of Laurent polynomials in two variables and B be the set of skew derivations of A. Let L be the universal central extension of the derived Lie subalgebra ofExpand
Automorphism group and twisted modules of the twisted Heisenberg-Virasoro vertex operator algebra
We first determine the automorphism group of the twisted Heisenberg-Virasoro vertex operator algebra $V_{\mathcal{L}}(\ell_{123},0)$.Then, for any integer $t>1$, we introduce a new Lie algebraExpand
Harish-Chandra modules for divergence zero vector fields on a torus
• Mathematics
• Pacific Journal of Mathematics
• 2019
Let $A=\mathbb{C}[t_1^{\pm1},t_2^{\pm1}]$ be the algebra of Laurent polynomials in two variables and $B$ be the set of skew derivations of $A$. Let $L$ be the universal central extension of theExpand

#### References

SHOWING 1-10 OF 43 REFERENCES
Q-Virasoro algebra and vertex algebras
• Mathematics
• 2014
Abstract In this paper, we study a certain deformation D of the Virasoro algebra that was introduced and called q-Virasoro algebra by Belov and Chaltikian, in the context of vertex algebras. AmongExpand
Free field realization of the twisted Heisenberg-Virasoro algebra at level zero and its applications
• Mathematics, Physics
• 2014
We investigate the free fields realization of the twisted Heisenberg-Virasoro algebra $\mathcal{H}$ at level zero. We completely describe the structure of the associated Fock representations. UsingExpand
Vertex Operator Algebras and the Monster
• Mathematics
• 2011
Lie Algebras. Formal Calculus: Introduction. Realizations of sl(2) by Twisted Vertex Operators. Realizations of sl(2) by Untwisted Vertex Operators. Central Extensions. The Simple Lie Algebras An,Expand
G-equivariant ϕ-coordinated quasi modules for quantum vertex algebras
This is a paper in a series to study quantum vertex algebras and their relations with various quantum algebras. In this paper, we introduce a notion of T-type quantum vertex algebra and a notion ofExpand
Nonlocal vertex algebras generated by formal vertex operators
Abstract.This is the first paper in a series to study vertex algebra-like objects arising from infinite-dimensional quantum groups (quantum affine algebras and Yangians). In this paper we lay theExpand
On certain generalizations of twisted affine Lie algebras and quasimodules for Γ-vertex algebras
Abstract We continue a previous study on Γ -vertex algebras and their quasimodules. In this paper we refine certain known results and we prove that for any Z -graded vertex algebra V and a positiveExpand
Howe pairs in the theory of vertex algebras
• Mathematics
• 2006
Abstract For any vertex algebra V and any subalgebra A ⊂ V , there is a new subalgebra of V known as the commutant of A in V . This construction was introduced by Frenkel–Zhu, and is a generalizationExpand
Vertex operator algebras associated to representations of affine and Virasoro Algebras
• Mathematics
• 1992
The first construction of the integrable highest-weight representations of affine Lie algebras or loop algebras by Kac i-K] was greatly inspired by the generalization of the Weyl denominator formulaExpand
Associating vertex algebras with the unitary Lie algebra
• Mathematics
• 2015
Abstract In this paper, we associate vertex algebras and their two different kinds of module categories with the unitary Lie algebra u ˆ N ( C Γ ˜ ) for N ≥ 2 being a positive integer and Γ ˜ = { q nExpand
Generalized vertex algebras and relative vertex operators
• Mathematics
• 1993
1. Introduction. 2. The setting. 3. Relative untwisted vertex operators. 4. Quotient vertex operators. 5. A Jacobi identity for relative untwisted vertex operators. 6. Generalized vertex operatorExpand