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1.
This paper reviews some recent results on the parafermion vertex operator algebra associated to the integrable highest weight
module L(k, 0) of positive integer level k for any affine Kac-Moody Lie algebra ĝ, where g is a finite dimensional simple Lie algebra. In particular, the generators and the C
2-cofiniteness of the parafermion vertex operator algebras are discussed. A proof of the well-known fact that the parafermion
vertex operator algebra can be realized as the commutant of a lattice vertex operator algebra in L(k, 0) is also given. 相似文献
2.
For a vertex operator algebra V with conformal vector ω,we consider a class of vertex operator subalgebras and their conformal vectors.They are called semi-conformal vertex operator subalgebras and semiconformal vectors of(V,ω),respectively,and were used to study duality theory of vertex operator algebras via coset constructions.Using these objects attached to(V,ω),we shall understand the structure of the vertex operator algebra(V,ω).At first,we define the set Sc(V,ω)of semi-conformal vectors of V, then we prove that Sc(V,ω)is an affine algebraic variety with a partial ordering and an involution map.Corresponding to each semi-conformal vector,there is a unique maximal semi-conformal vertex operator subalgebra containing it.The properties of these subalgebras are invariants of vertex operator algebras.As an example,we describe the corresponding varieties of semi-conformal vectors for Heisenberg vertex operator algebras.As an application,we give two characterizations of Heisenberg vertex operator algebras using the properties of these varieties. 相似文献
3.
Twisted representations of vertex operator algebras 总被引:7,自引:0,他引:7
4.
Let V be a vertex operator algebra and m, n ≥ 0. We construct an A
n
(V)-A
m
(V)-bimodule A
n,m
(V) which determines the action of V from the level m subspace to level n subspace of an admissible V-module. We show how to use A
n,m
(V) to construct naturally admissible V-modules from A
m
(V)-modules. We also determine the structure of A
n,m
(V) when V is rational.
Chongying Dong was supported by NSF grants, China NSF grant 10328102 and a Faculty research grant from the University of California
at Santa Cruz. Cuipo Jiang was supported in part by China NSF grant 10571119. 相似文献
5.
Ching Hung Lam 《代数通讯》2013,41(14):4339-4360
Given a commutative associative algebra A with an associative form (’), we construct a vertex operator algebra V with the weight two space V2;? A If in addition the form (’) is nondegenerate, we show that there is a simple vertex operator algebra with V2;? A We also show that if A is semisimple, then the vertex operator algebra constructed is the tensor products of a certain number of Virasoro vertex operator algebras. 相似文献
6.
7.
Chin Hung Lam 《代数通讯》2013,41(9):4587-4605
8.
Gerald Höhn 《Advances in Mathematics》2008,217(5):2301-2335
We introduce the notion of a conformal design based on a vertex operator algebra. This notation is a natural analog of the notion of block designs or spherical designs when the elements of the design are based on self-orthogonal binary codes or integral lattices, respectively. It is shown that the subspaces of an extremal self-dual vertex operator algebra of fixed degree form conformal 11-, 7-, or 3-designs, generalizing similar results of Assmus and Mattson and Venkov for extremal doubly-even codes and extremal even lattices. Other examples are coming from group actions on vertex operator algebras, the case studied first by Matsuo. The classification of conformal 6- and 8-designs is investigated. Again, our results are analogous to similar results for codes and lattices. 相似文献
9.
Katrina Barron Nathan Vander Werf Jinwei Yang 《Journal of Pure and Applied Algebra》2019,223(8):3295-3317
Motivated by the study of indecomposable, nonsimple modules for a vertex operator algebra V, we study the relationship between various types of V-modules and modules for the higher level Zhu algebras for V, denoted , for , first introduced by Dong, Li, and Mason in 1998. We resolve some issues that arise in a few theorems previously presented when these algebras were first introduced, and give examples illustrating the need for certain modifications of the statements of those theorems. We establish that whether or not is isomorphic to a direct summand of affects the types of indecomposable V-modules which can be constructed by inducing from an -module, and in particular whether there are V-modules induced from -modules that were not already induced by . We give some characterizations of the V-modules that can be constructed from such inducings, in particular as regards their singular vectors. To illustrate these results, we discuss two examples of : when V is the vertex operator algebra associated to either the Heisenberg algebra or the Virasoro algebra. For these two examples, we show how the structure of in relationship to determines what types of indecomposable V-modules can be induced from a module for the level zero versus level one Zhu algebras. We construct a family of indecomposable modules for the Virasoro vertex operator algebra that are logarithmic modules and are not highest weight modules. 相似文献
10.
Modular invariance of characters of vertex operator algebras 总被引:19,自引:0,他引:19
Yongchang Zhu 《Journal of the American Mathematical Society》1996,9(1):237-302
11.
In this paper, for a vertex operator algebra V with an automorphism g of order T, an admissible V-module M and a fixed nonnegative rational number n ∈1/T Z_+, we construct an A_(g,n)(V)-bimodule Ag,n(M) and study its properties, discuss the connections between bimodule A_(g,n)(M) and intertwining operators. Especially, bimodule A _(g,n)-1T(M) is a natural quotient of A_(g,n)(M) and there is a linear isomorphism between the space IM~k M Mjof intertwining operators and the space of homomorphisms HomA_(g,n)(V)(A_(g,n)(M) A_(g,n)(V)M~j(s), M~k(t)) for s, t ≤ n, M~j, M~k are g-twisted V modules, if V is g-rational. 相似文献
12.
13.
14.
《Journal of Pure and Applied Algebra》1994,96(3):279-297
We give a criterion for determining the existence of nonzero symmetric invariant bilinear forms on vertex operator algebras and we establish an analogue of the Cartan criterion for semi-simplicity. 相似文献
15.
If a vertex operator algebra satisfies , , then has a commutative (nonassociative) algebra structure called Griess algebra. One of the typical examples of commutative (nonassociative) algebras is a Jordan algebra. For example, the set of symmetric matrices of degree d becomes a Jordan algebra. On the other hand, in the theory of vertex operator algebras, central charges influence the properties of vertex operator algebras. In this paper, we construct vertex operator algebras with central charge c and its Griess algebra is isomorphic to for any complex number c and a positive integer d. 相似文献
16.
S. E. Klevtsov 《Theoretical and Mathematical Physics》2008,154(2):201-208
We describe a construction of the quantum-deformed affine algebras using vertex operators in the free field theory. We prove
the Serre relations for the Borel subalgebras of quantum affine algebras; in particular, we consider the
case in detail. We also construct the generators corresponding to the positive roots of
.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 2, pp. 240–248, February, 2008. 相似文献
17.
J. M. G. Fell 《Acta Mathematica》1961,106(3-4):233-280
18.
We apply an idea of framed vertex operator algebras to a construction of local conformal nets of (injective type III1) factors on the circle corresponding to various lattice vertex operator algebras and their twisted orbifolds. In particular, we give a local conformal net corresponding to the moonshine vertex operator algebras of Frenkel-Lepowsky-Meurman. Its central charge is 24, it has a trivial representation theory in the sense that the vacuum sector is the only irreducible DHR sector, its vacuum character is the modular invariant J-function and its automorphism group (the gauge group) is the Monster group. We use our previous tools such as α-induction and complete rationality to study extensions of local conformal nets. 相似文献
19.