• Corpus ID: 250408114

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}
}
  • Fei Qi
  • Published 8 July 2022
  • Mathematics
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… 
1 Citations

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References

SHOWING 1-10 OF 20 REFERENCES

On modules for meromorphic open-string vertex algebras

  • Fei Qi
  • Mathematics
    Journal 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

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

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.

  • R. Borcherds
  • Mathematics
    Proceedings 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

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

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

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

  • Fei Qi
  • Mathematics
    Letters 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

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

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