• Corpus ID: 119142989

# A construction of admissible $A_1^{(1)}$-modules of level $-{4/3}$

@article{Adamovi2004ACO,
title={A construction of admissible \$A\_1^\{(1)\}\$-modules of level \$-\{4/3\}\$},
journal={arXiv: Quantum Algebra},
year={2004}
}
By using generalized vertex algebras associated to rational lattices, we construct explicitly the admissible modules for the affine Lie algebra $A_1 ^{(1)}$ of level $-{4/3}$. As an application, we show that the W(2,5) algebra with central charge c=-7 investigated in math.QA/0207155 is a subalgebra of the simple affine vertex operator algebra $L(-{4/3}\Lambda_0)$.
66 Citations

### Vertex operator algebras associated to certain admissible modules for affine Lie algebras of type A

Let $L(-{1/2}(l+1),0)$ be the simple vertex operator algebra associated to an affine Lie algebra of type $A_{l}^{(1)}$ with the lowest admissible half-integer level $-{1/2}(l+1)$, for even l. We

### A note on representations of some affine vertex algebras of type D

In this note we construct a series of singular vectors in universal affine vertex operator algebras associated to $D_{\ell}^{(1)}$ of levels $n-\ell+1$, for $n \in \Z_{>0}$. For $n=1$, we study the

### Lie Superalgebras and Irreducibility of $$A_1^{(1)}$$ –Modules at the Critical Level

We introduce the infinite-dimensional Lie superalgebra $${\mathcal{A}}$$ and construct a family of mappings from a certain category of $${\mathcal{A}}$$ –modules to the category of $${A_1^{(1)}}$$

### A REALIZATION OF CERTAIN MODULES FOR THE N = 4 SUPERCONFORMAL ALGEBRA AND THE AFFINE LIE ALGEBRA A2(1)

We shall first present an explicit realization of the simple N = 4 superconformal vertex algebra LcN = 4 with central charge c = −9. This vertex superalgebra is realized inside of the bcβγ system and

### On Infinite Order Simple Current Extensions of Vertex Operator Algebras

• Mathematics
• 2017
We construct a direct sum completion $\mathcal{C}_{\oplus}$ of a given braided monoidal category $\mathcal{C}$ which allows for the rigorous treatment of infinite order simple current extensions of

### Realizations of simple affine vertex algebras and their modules: the cases $\widehat{sl(2)}$ and $\widehat{osp(1,2)}$

We study embeddings of the simple admissible affine vertex algebras $V_k(sl(2))$ and $V_k(osp(1,2))$, $k \notin {\Bbb Z}_{\ge 0}$, into the tensor product of rational Virasoro and $N=1$ Neveu-Schwarz

### Admissible-level $$\mathfrak {sl}_3$$ minimal models

• Mathematics
Letters in Mathematical Physics
• 2022
. The ﬁrst part of this work uses the algorithm recently detailed in [1] to classify the irreducible weight modules of the minimal model vertex operator algebra L k ( 𝔰𝔩 3 ) , when the level k is

### Lattice construction of logarithmic modules for certain vertex algebras

• Mathematics
• 2009
A general method for constructing logarithmic modules in vertex operator algebra theory is presented. By utilizing this approach, we give explicit vertex operator construction of certain

### Coset Constructions of Logarithmic (1, p) Models

• Mathematics
• 2013
One of the best understood families of logarithmic onformal field theories consists of the (1, p) models (p =  2, 3, . . .) of central charge c1, p=1 − 6(p − 1)2/p. This family includes the theories

## References

SHOWING 1-10 OF 32 REFERENCES

### Vertex operator algebras associated to modular invariant representations for $A_1 ^{(1)}$

• Mathematics
• 1995
We investigate vertex operator algebras $L(k,0)$ associated with modular-invariant representations for an affine Lie algebra $A_1 ^{(1)}$ , where k is 'admissible' rational number. We show that VOA

### Vertex Operator Algebras Associated to Admissible Representations of

• Mathematics
• 1995
Abstract: The Kac-Wakimoto admissible modules for $\hat{sl}_2$ are studied from the point of view of vertex operator algebras. It is shown that the vertex operator algebra L(l,0) associated to

### Annihilating fields of standard modules of sl(2, C)~ and combinatorial identies

• Mathematics
• 1998
We show that a set of local admissible fields generates avertex algebra. For an affine Lie algebra $ildegoth g$ we construct the corresponding level $k$ vertex operator algebra and we show that

### REPRESENTATIONS OF THE VERTEX ALGEBRA W 1+∞ WITH A NEGATIVE INTEGER CENTRAL CHARGE

Let D be the Lie algebra of regular differential operators on , and be the central extension of D. Let W 1+∞,minus;N be the vertex algebra associated to the irreducible vacuum -module with the

### Representation theory of the vertex algebraW1+∞

• Mathematics
• 1996
In our paper [KR] we began a systematic study of representations of the universal central extension of the Lie algebra of differential operators on the circle. This study was continued in the paper

### Modular invariant representations of infinite-dimensional Lie algebras and superalgebras.

• Mathematics
Proceedings of the National Academy of Sciences of the United States of America
• 1988
It is shown that the modular invariant representations of the Virasoro algebra Vir are precisely the "minimal series" of Belavin et al.

### Algebra, Algebra, and Friedan–Martinec–Shenker Bosonization

Abstract:We show that the vertex algebra with central charge − 1 is isomorphic to a tensor product of the simple algebra with central charge − 2 and a Heisenberg vertex algebra generated by a free