共查询到20条相似文献,搜索用时 31 毫秒
1.
Haisheng Li 《Communications in Mathematical Physics》2001,217(3):653-696
We generalize Feigin and Miwa's construction of extended vertex operator (super)algebras A
k
(sl(2)) for other types of simple Lie algebras. For all the constructed extended vertex operator (super)algebras, irreducible
modules are classified, complete reducibility of every module is proved and fusion rules are determined modulo the fusion
rules for vertex operator algebras of affine type.
Received: 7 March 2000 / Accepted: 10 November 2000 相似文献
2.
P. Bowcock B. L. Feigin A. M. Semikhatov A. Taormina 《Communications in Mathematical Physics》2000,214(3):495-545
We discover a realisation of the affine Lie superalgebra and of the exceptional affine superalgebra as vertex operator extensions of two algebras with “dual” levels (and an auxiliary level-1 algebra). The duality relation between the levels is . We construct the representation of on a sum of tensor products of , , and modules
and decompose it into a direct sum over the spectral flow orbit. This decomposition gives rise to character identities, which we also derive. The extension of the construction
to is traced to the properties of embeddings into and their relation with the dual pairs. Conversely, we show how the representations are constructed from representations.
Received: 29 July 1999 / Accepted: 6 February 2000 相似文献
3.
Haisheng Li 《Communications in Mathematical Physics》2010,296(2):475-523
This is a paper in a series to study vertex algebra-like structures arising from various algebras including quantum affine
algebras and Yangians. In this paper, we study notions of (h/2p){\hbar}-adic nonlocal vertex algebra and (h/2p){\hbar}-adic (weak) quantum vertex algebra, slightly generalizing Etingof-Kazhdan’s notion of quantum vertex operator algebra. For
any topologically free
\mathbb C[[(h/2p)]]{{\mathbb C}\lbrack\lbrack{\hbar}\rbrack\rbrack}-module W, we study (h/2p){\hbar}-adically compatible subsets and (h/2p){\hbar}-adically S{\mathcal{S}}-local subsets of (End W)[[x, x
−1]]. We prove that any (h/2p){\hbar}-adically compatible subset generates an (h/2p){\hbar}-adic nonlocal vertex algebra with W as a module and that any (h/2p){\hbar}-adically S{\mathcal{S}}-local subset generates an (h/2p){\hbar}-adic weak quantum vertex algebra with W as a module. A general construction theorem of (h/2p){\hbar}-adic nonlocal vertex algebras and (h/2p){\hbar}-adic quantum vertex algebras is obtained. As an application we associate the centrally extended double Yangian of
\mathfrak s\mathfrak l2{{\mathfrak s}{\mathfrak l}_{2}} to (h/2p){\hbar}-adic quantum vertex algebras. 相似文献
4.
Haisheng Li 《Communications in Mathematical Physics》2011,308(3):703-741
We develop a theory of f{\phi} -coordinated (quasi-) modules for a general nonlocal vertex algebra where f{\phi} is what we call an associate of the one-dimensional additive formal group. By specializing f{\phi} to a particular associate, we obtain a new construction of weak quantum vertex algebras in the sense of Li (Selecta Mathematica
(New Series) 11:349–397, 2005). As an application, we associate weak quantum vertex algebras to quantum affine algebras, and we also associate quantum
vertex algebras and f{\phi} -coordinated modules to a certain quantum βγ-system explicitly. 相似文献
5.
Fundamental representations of the Euclidean Lie algebra A
2l
(2)
is constructed by decomposing the vertex representations of gI(∞). For l=1 the multiplicities of highest weights are determined. Soliton equations associated with each of these representations are
also discussed. 相似文献
6.
A general construction of an sh Lie algebra (L
∞-algebra) from a homological resolution of a Lie algebra is given. It is applied to the space of local functionals equipped
with a Poisson bracket, induced by a bracket for local functions along the lines suggested by Gel'fand, Dickey and Dorfman.
In this way, higher order maps are constructed which combine to form an sh Lie algebra on the graded differential algebra
of horizontal forms. The same construction applies for graded brackets in field theory such as the Batalin-Fradkin-Vilkovisky
bracket of the Hamiltonian BRST theory or the Batalin-Vilkovisky antibracket.
Received: 5 March 1997 / Accepted: 21 May 1997 相似文献
7.
Hirofumi Yamada 《Letters in Mathematical Physics》1985,9(2):133-137
Tensor product of the basic representation of the extended affine Lie algebra of type A
inf1
sup(1)
is discussed through the vertex operator of {ie133-1}. The highest irreducible component of the tensor product is characterized by the BKP hierarchy. 相似文献
8.
Generalizations of the q-Onsager algebra are introduced and studied. In one of the simplest case and q = 1, the algebra reduces to the one proposed by Uglov–Ivanov. In the general case and q ≠ 1, an explicit algebra homomorphism associated with coideal subalgebras of quantum affine Lie algebras (simply and non-simply
laced) is exhibited. Boundary (soliton non-preserving) integrable quantum Toda field theories are then considered in light
of these results. For the first time, all defining relations for the underlying non-Abelian symmetry algebra are explicitly
obtained. As a consequence, based on purely algebraic arguments all integrable (fixed or dynamical) boundary conditions are
classified. 相似文献
9.
André Lichnerowicz 《Letters in Mathematical Physics》1979,3(6):495-502
The twisted products play an important role in Quantum Mechanics [1, 2]. We introduce here a distinction between Vey *ν-products and strong Vey *ν-products and prove that each *ν-product is equivalent to a Vey *ν-product. If b
3(W)=0, the symplectic manifold (W, F) admits strong Vey *ν-products. If b
2(W)=0, all *ν-products are equivalent as well as the Vey Lie algebras. In the general case, we characterize the formal Lie algebras which
are generated by a *ν-product and we prove that the existence of a *ν-product is equivalent to the existence of a formal Lie algebra infinitesimally equivalent to a Vey Lie algebra at the first
order. 相似文献
10.
Hong Wei Yang Bao Shu Yin Yong Fang 《International Journal of Theoretical Physics》2011,50(3):671-681
A class of new Lie algebra B
3 is constructed, which is far different from the known Lie algebra A
n−1. Based on the corresponding loop algebra [(B3)\tilde]\tilde{B_{3}}, the generalized mKdV hierarchy is established. In order to look for the Hamiltonian structure of such integrable system,
a generalized trace functional of matrices is introduced, whose special case is just the well-known trace identity. Finally,
its expanding integrable model is worked out by use of an enlarged Lie algebra. 相似文献
11.
In Torossian (J Lie Theory 12(2):597–616, 2002), the second author used the Kontsevich deformation quantization technique
to define a natural connection ω
n
on the compactified configuration spaces [`(C)]n,0{\overline{C}_{n,0}} of n points on the upper half-plane. Connections ω
n
take values in the Lie algebra of derivations of the free Lie algebra with n generators. In this paper, we show that ω
n
is flat. 相似文献
12.
We consider the sine-Gordon and affine Toda field theories on the half-line with classically integrable boundary conditions,
and show that in the quantum theory a remnant survives of the bulk quantized affine algebra symmetry generated by non-local
charges. The paper also develops a general framework for obtaining solutions of the reflection equation by solving an intertwining
property for representations of certain coideal subalgebras of U
q
(ĝ).
Received: 10 December 2001 / Accepted: 7 October 2002 Published online: 19 December 2002 相似文献
13.
By quantizing the generalized Drinfeld-Sokolov reduction scheme for arbitrarysl
2 embeddings we show that a large set of quantumW algebras can be viewed as (BRST) cohomologies of affine Lie algebras. The set contains many knownW algebras such asW
N
andW
3
(2)
. Our formalism yields a completely algorithmic method for calculating theW algebra generators and their operator product expansions, replacing the cumbersome construction ofW algebras as commutants of screening operators. By generalizing and quantizing the Miura transformation we show that anyW algebra in can be embedded into the universal enveloping algebra of a semisimple affine Lie algebra which is, up to shifts in level, isomorphic to a subalgebra of the original affine algebra. Thereforeany realization of this semisimple affine Lie algebra leads to a realization of theW algebra. In particular, one obtains in this way a general and explicit method for constructing the free field realizations and Fock resolusions for all algebras in. Some examples are explicitly worked out. 相似文献
14.
15.
In this paper, we study McKay’s E
6-observation on the largest Fischer 3-transposition group Fi24. We investigate a vertex operator algebra
VF\natural{VF^{\natural}} of central charge
23\frac15{23\frac{1}{5}} on which the Fischer group Fi24 naturally acts. We show that there is a natural correspondence between dihedral subgroups of Fi24 and certain vertex operator subalgebras constructed by the nodes of the affine E
6 diagram by investigating so-called derived Virasoro vectors of central charge 6/7. This allows us to reinterpret McKay’s
E
6-observation via the theory of vertex operator algebras. 相似文献
16.
Chiral orbifold models are defined as gauge field theories with a finite gauge group Γ. We start with a conformal current
algebra associated with a connected compact Lie group G and a negative definite integral invariant bilinear form on its Lie algebra. Any finite group Γ of inner automorphisms or
(in particular, any finite subgroup of G) gives rise to a gauge theory with a chiral subalgebra of local observables invariant under Γ. A set of positive energy modules is constructed whose characters span, under some assumptions on Γ, a finite dimensional unitary representation of
. We compute their asymptotic dimensions
(thus singling out the nontrivial orbifold modules) and find explicit formulae for the modular transformations and hence,
for the fusion rules.
As an application we construct a family of rational conformal field theory (RCFT) extensions of W
1+∞ that appear to provide a bridge between two approaches to the quantum Hall effect.
Received: 5 December 1996 / Accepted: 1 April 1997 相似文献
17.
P. Moylan 《Czechoslovak Journal of Physics》1997,47(12):1251-1258
We show that it is possible to express the basis elements of the Lie algebra of the Euclidean group,E(2), as simple irrational functions of certainq deformed expressions involving the generators of the quantum algebraU
q
(so(2, 1)). We consider implications of these results for the representation theory of the Lie algebra ofE(2). We briefly discess analogous results forU
q
(so(2, 2)).
Presented at the 6th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 19–21 June
1997. 相似文献
18.
V. N. Tolstoy 《Czechoslovak Journal of Physics》2001,51(12):1453-1458
Tensor operators are discussed for Hopf algebras and, in particular, for a quantum (q-deformed) algebraUq(g), whereg is any simple finite-dimensional or affine Lie algebra. These operators are defined via an adjoint action in a Hopf algebra.
There are two types of the tensor operators which correspond to two coproducts in the Hopf algebra. In the case of tensor
products of two tensor operators one can obtain 8 types of the tensor operators and so on. We prove the relations which can
be a basis for a proof of the Wigner-Eckart theorem for the Hopf algebras. It is also shown that in the case ofUq(g) a scalar operator can be differed from an invariant operator but atq=1 these operators coincide.
Presented at the 10th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 21–23 June
2001.
Supported by Russian Foundation for Fundamental Research, grant 99-01-01163, and by INTAS-00-00055. 相似文献
19.
Chongying Dong Haisheng Li Geoffrey Mason 《Communications in Mathematical Physics》1996,180(3):671-707
We consider how a vertex operator algebra can be extended to an abelian interwining algebra by a family of weak twisted modules which aresimple currents associated with semisimple weight one primary vectors. In the case that the extension is again a vertex operator algebra, the rationality of the extended algebra is discussed. These results are applied to affine Kac-Moody algebras in order to construct all the simple currents explicitly (except forE
8) and to get various extensions of the vertex operator algebras associated with integrable representations.Supported by NSF grant DMS-9303374 and a research grant from the Committee on Research, UC Santa Cruz.Supported by NSF grant DMS-9401272 and a research grant from the Committee on Research, UC Santa Cruz. 相似文献
20.
In this paper the W-algebra W(2, 2) and its representation theory are studied. It is proved that a simple vertex operator algebra generated by two weight
2 vectors is either a vertex operator algebra associated to an irreducible highest weight W(2, 2)- module or a tensor product of two simple Virasoro vertex operator algebras. Furthermore, we show that any rational,
C
2-cofinite and simple vertex operator algebra whose weight 1 subspace is zero, weight 2 subspace is 2-dimensional and with
central charge c = 1 is isomorphic to .
Supported by NSF grants and a research grant from the Committee on Research, UC Santa Cruz. 相似文献