# 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} }

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

- Mathematics
- 2021

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 highest… Expand

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 of… Expand

Automorphism group and twisted modules of the twisted Heisenberg-Virasoro vertex operator algebra

- Physics, Mathematics
- 2020

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 algebra… Expand

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 the… Expand

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