# On the extensions of the left modules for a meromorphic open-string vertex algebra, I

@inproceedings{Qi2022OnTE, title={On the extensions of the left modules for a meromorphic open-string vertex algebra, I}, author={Fei Qi}, year={2022} }

We study the extensions of two left modules W1,W2 for a meromorphic open-string vertex algebra V . We show that the extensions satisfying some technical but natural convergence conditions are in bijective correspondence to the first cohomology classes associated to the V bimodule HN (W1,W2) constructed in [HQ]. When V is grading-restricted and contains a nice vertex subalgebra V0, those convergence conditions hold automatically. In addition, we show that the dimension of Ext(W1,W2) is bounded…

## One Citation

### Convergence in Conformal Field Theory

- MathematicsChinese Annals of Mathematics, Series B
- 2022

Convergence and analytic extension are of fundamental importance in the mathematical construction and study of conformal field theory. The author reviews some main convergence results, conjectures…

## References

SHOWING 1-10 OF 20 REFERENCES

### On modules for meromorphic open-string vertex algebras

- MathematicsJournal of Mathematical Physics
- 2019

This paper generalizes Huang's cohomology theory of grading-restricted vertex algebras to meromorphic open-string vertex algebras (MOSVAs hereafter), which are noncommutative generalizations of…

### On the cohomology of meromorphic open-string vertex algebras

- Mathematics
- 2019

This paper generalizes Huang’s cohomology theory of grading restricted vertex algebras to meromorphic open-string vertex algebras (MOSVAs hereafter), which are noncommutative generalizations of…

### Meromorphic open-string vertex algebras

- Mathematics
- 2013

A notion of meromorphic open-string vertex algebra is introduced. A meromorphic open-string vertex algebra is an open-string vertex algebra in the sense of Kong and the author satisfying additional…

### Vertex algebras, Kac-Moody algebras, and the Monster.

- MathematicsProceedings of the National Academy of Sciences of the United States of America
- 1986

An integral form is constructed for the universal enveloping algebra of any Kac-Moody algebras that can be used to define Kac's groups over finite fields, some new irreducible integrable representations, and a sort of affinization of anyKac-moody algebra.

### A Cohomology Theory of Grading-Restricted Vertex Algebras

- Mathematics
- 2010

We introduce a cohomology theory of grading-restricted vertex algebras. To construct the correct cohomologies, we consider linear maps from tensor powers of a grading-restricted vertex algebra to…

### Tensor categories of affine Lie algebras beyond admissible levels

- Mathematics
- 2020

We show that if V is a vertex operator algebra such that all the irreducible ordinary V -modules are $$C_1$$ C 1 -cofinite and all the grading-restricted generalized Verma modules for V are of finite…

### On the Structure of Verma Modules over Virasoro and Neveu-Schwarz Algebras

- Mathematics
- 1995

Abstract:In the paper we present a different proof of the theorem of B. L. Feigin and D. B. Fuchs about the structure of Verma modules over Virasoro algebra. We state some new results about the…

### Meromorphic open-string vertex algebras and modules over two-dimensional orientable space forms

- MathematicsLetters in Mathematical Physics
- 2021

We study the meromorphic open-string vertex algebras and their modules over the two-dimensional Riemannian manifolds that are complete, connected, orientable, and of constant sectional curvature…

### First and Second Cohomologies of Grading-Restricted Vertex Algebras

- Mathematics
- 2010

Let V be a grading-restricted vertex algebra and W a V-module. We show that for any $${m\in \mathbb{Z}_{+}}$$m∈Z+, the first cohomology $${H^{1}_{m}(V, W)}$$Hm1(V,W) of V with coefficients in W…

### Braided Tensor Categories and Extensions of Vertex Operator Algebras

- Mathematics
- 2014

Let V be a vertex operator algebra satisfying suitable conditions such that in particular its module category has a natural vertex tensor category structure, and consequently, a natural braided…