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A class of weight modules over the twisted Heisenberg-Virasoro algebra and gap-$p$ Virasoro algebras

Chengkang Xu, Fen Zhang

Abstract

In this paper, we construct a class of simple weight modules over the twisted Heisenberg-Virasoro algebra and gap-$p$ Virasoro algebras from restricted modules over some positive part subalgebra of the twisted Heisenberg-Virasoro algebra. These modules are new. In particular, when $p=2$, the gap-$p$ Virasoro algebra is the mirror Heisenberg-Virasoro algebra and we obtain many new simple weight modules for the mirror Heisenberg-Virasoro algebra.

A class of weight modules over the twisted Heisenberg-Virasoro algebra and gap-$p$ Virasoro algebras

Abstract

In this paper, we construct a class of simple weight modules over the twisted Heisenberg-Virasoro algebra and gap- Virasoro algebras from restricted modules over some positive part subalgebra of the twisted Heisenberg-Virasoro algebra. These modules are new. In particular, when , the gap- Virasoro algebra is the mirror Heisenberg-Virasoro algebra and we obtain many new simple weight modules for the mirror Heisenberg-Virasoro algebra.
Paper Structure (6 sections, 10 theorems, 55 equations)

This paper contains 6 sections, 10 theorems, 55 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Constructing weight modules
  4. Isomorphism classes
  5. The modules are new
  6. Some irreducible non-weight modules

Key Result

Proposition 3.1

(1) The actions in T-action make $V\otimes\mathbb C[x^{\pm1}]$ a weight ${\mathbb{T}}$-module. (2) The actions in g-action make $V\otimes\mathbb C[P]$ a weight $\mathfrak{g}$-module.

Theorems & Definitions (28)

  • Definition 2.1
  • Definition 2.2
  • Remark 2.3
  • Definition 2.4
  • Remark 2.5
  • Definition 2.6
  • Proposition 3.1
  • proof
  • Lemma 3.2
  • proof
  • ...and 18 more