共查询到20条相似文献,搜索用时 15 毫秒
1.
Bruce N. Allison Stephen Berman Yun Gao Arturo Pianzola 《Communications in Mathematical Physics》1997,185(3):671-688
We give a new characterization of the affine Kac-Moody algebras in terms of extended affine Lie algebras. We also present
new realizations of the twisted affine Kac-Moody algebras.
Received: 17 April 1996 / Accepted: 11 October 1996 相似文献
2.
Explicit Fock representations of the classical Lie algebras in terms of boson creation and annihilation operators with an arbitrary highest weight are derived, and a general rule to construct Fock represen tations of a loop algebra from a boson realization ofits corresponding Lie algebra is establislted. A new kind of lowest weight represen tations of the affine Lie algebras attached to the classical Lie algebras, which require a zero center, is also presented. Based on these, a simple affinization procedure is given to obtain the Fock representations of level 1 of these affine Lie algebras. 相似文献
3.
For any finite-dimensional semisimple Lie algebra g, a
Z+-graded vertex algebra is construsted on the vacuum
representation Vk(\hat{g}[ θ]) of \hat{g}[θ], which is
a one-dimentional central extension of θ-invariant subspace on the loop algebra
Lg=g\otimes C((t1/p)). 相似文献
4.
DING Lu ZHENG Zhu-Jun 《理论物理通讯》2008,50(7):7-12
For any finite-dimensional semisimple Lie algebra g, a Z+-graded vertex algebra is construsted on the vacuum representation Vk(g[θ]of g[θ]),which is a one-dimentionM central extension of 8-invariant subspace on the loop algebra Lg=g C((t^1/p)). 相似文献
5.
《Journal of Geometry and Physics》1988,5(2):209-235
The homology of the Lie algebra of algebraic vector fields in the complex line with trivial 3-jet at the point 0 with the coefficients in irreducible highest weight representations of the Virasoro Lie algebra is calculated. The same is done for vector fields with trivial 1-jets at two distinguished points. The class of quasi- finite representations of the Virasoro Lie algebra naturally arises which is the substitute for the class of finite-dimensional representations. The similar results for Kac-Moody Lie algebras are given as well as some conjectures and announcements. 相似文献
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Atsushi Nakayashiki 《Communications in Mathematical Physics》2003,240(1-2):197-241
We study certain subspaces of solutions to the sl2 rational qKZ equation at level zero. Each subspace is specified by the vanishing of the residue at a certain divisor which stems from models in two dimensional integrable field theories. We determine the character of the subspace which is parametrized by the number of variables and the sl2 weight of the solutions. The sum of all characters with a fixed weight gives rise to the branching functions of the irreducible representations of sl2 in the level one integrable highest weight representations of . It is written in the fermionic form. 相似文献
10.
In two earlier articles we constructed algebraic-geometric families of genus one (i.e. elliptic) Lie algebras of Krichever–Novikov
type. The considered algebras are vector fields, current and affine Lie algebras. These families deform the Witt algebra,
the Virasoro algebra, the classical current, and the affine Kac–Moody Lie algebras respectively. The constructed families
are not equivalent (not even locally) to the trivial families, despite the fact that the classical algebras are formally rigid.
This effect is due to the fact that the algebras are infinite dimensional. In this article the results are reviewed and developed
further. The constructions are induced by the geometric process of degenerating the elliptic curves to singular cubics. The
algebras are of relevance in the global operator approach to the Wess–Zumino–Witten–Novikov models appearing in the quantization
of Conformal Field Theory. 相似文献
11.
José Alberty Anne Taormina Pierre van Baal 《Communications in Mathematical Physics》1988,120(2):249-260
We demonstrate that the Kac-Moody and Virasoro-like algebras on Riemann surfaces of arbitrary genus with two punctures introduced by Krichever and Novikov are in two ways linearly related to Kac-Moody and Virasoro algebras onS
1. The two relations differ by a Bogoliubov transformation, and we discuss the connection with the operator formalism. 相似文献
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We study representations of affine Kac-Moody algebras from a geometric point of view. It is shown that Wakimoto modules introduced in [18], which are important in conformal field theory, correspond to certain sheaves on a semi-infinite flag manifold with support on its Schhubert cells. This manifold is equipped with a remarkable semi-infinite structure, which is discussed; in particular, the semi-infinite homology of this manifold is computed. The Cousin-Grothendieck resolution of an invertible sheaf on a semi-infinite flag manifold gives a two-sided resolution of an irreducible representation of an affine algebras, consisting of Wakimoto modules. This is just the BRST complex. As a byproduct we compute the homology of an algebra of currents on the real line with values in a nilpotent Lie algebra.Dedicated to Dmitry Borisovich Fuchs on his 50th birthdayAddress after September 15, 1989: Mathematics Department, Harvard University, Cambrdige, MA 02138, USA 相似文献
14.
Askar Dzhumadil’daev 《Zeitschrift fur Physik C Particles and Fields》1996,72(3):509-517
The first and second cohomologies of Cartan Type Lie algebras with coefficients in irreducible tensor modules are calculated. The spaceH 1(L, U) is interpreted as a space of deformations of (L, U)-modules.H 2(L, L)≠0 ifL=S 2,S 2 + orL=H n ,H n + . Lie algebra of divergenceless vector fieldsS 2 + has only one nontrivial local deformation. The two-sided simple hamiltonian algebraH n has 2n 2+n new local deformations in addition to Moyal cocycle. The Lie algebrasL=W n (n>3),S n?1(n>2),H n (n>1),K n+1(n>1) have 3, 1, 1, 3 nonisomorphic tensor modules with irreducible bases and nonzero 1-cohomologies; respectively, the corresponding numbers for 2-cohomologies are 9, 6, 7 and 9. 相似文献
15.
This paper analyzes the action δ of a Lie algebra X by derivations on a C*–algebra ${\mathcal{A}}$ . This action satisfies an “almost inner” property which ensures affiliation of the generators of the derivations δ with ${\mathcal{A}}$ , and is expressed in terms of corresponding pseudo–resolvents. In particular, for an abelian Lie algebra X acting on a primitive C*–algebra ${\mathcal{A}}$ , it is shown that there is a central extension of X which determines algebraic relations of the underlying pseudo–resolvents. If the Lie action δ is ergodic, i.e. the only elements of ${\mathcal{A}}$ on which all the derivations in δ X vanish are multiples of the identity, then this extension is given by a (non–degenerate) symplectic form σ on X. Moreover, the algebra generated by the pseudo–resolvents coincides with the resolvent algebra based on the symplectic space (X, σ). Thus the resolvent algebra of the canonical commutation relations, which was recently introduced in physically motivated analyses of quantum systems, appears also naturally in the representation theory of Lie algebras of derivations acting on C*–algebras. 相似文献
16.
We discuss the dynamical structure of the semidirect product of the Virasoro and affine Kac-Moody groups within the framework of a group quantization formalism. This formalism provides a realization of the Virasoro algebra acting on Kac-Moody Fock states which generalizes the Sugawara construction. We also give an explicit construction of the standard Kac-Moody group representations associated with strings on SU(2) and recover, in particular, the renormalization factor of L(z)
Research partially supported by the Conselleria de Cultura de la Generalitat Valenciana, the Plan de Formacion del Personal Investigador, the Comision Asesora de Investigacion Cientifica y Tecnica (CAICYT), and The British Council. 相似文献
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We describe a method for obtaining Formal Group Laws from the structure constants of Affine Kac-Moody groups and then apply a group manifold quantization procedure which permits construction of physical representations by using only canonical structures on the group. As an intermediate step we get an explicit expression for two-cocycles on Loop Groups. The programme is applied to the AffineSU(2) group.Research partially supported by the Conselleria de Cultura de la Generalitat Valenciana, the Plan de Formacion del Personal Investigador, and the Comision Asesora de Investigacion Cientifica y Tecnica (CAICYT)On leave of absence from the IFIC, Centro Mixto Universidad de Valencia — C.S.I.C. and the Departamento de Fisica Teorica de la Universidad de Valencia 相似文献
19.
Josef Tkadlec 《International Journal of Theoretical Physics》2010,49(12):3279-3285
Connections between the weak orthocompleteness and the maximality property in effect algebras are presented. It is proved
that an orthomodular poset with the maximality property is disjunctive. A characterization of Archimedean weakly orthocomplete
effect algebras is given. 相似文献
20.
A 3? 3 matrix Lie algebra is first introduced, its subalgebras and the generated Lie algebras are obtained, respectively. Applications of a few Lie subalgebras give rise to two integrable nonlinear hierarchies of evolution equations from their reductions we obtain the nonlinear Schrödinger equations, the mKdV equations, the Broer-Kaup (BK) equation and its generalized equation, etc. The linear and nonlinear integrable couplings of one integrable hierarchy presented in the paper are worked out by casting a 3? 3 Lie subalgebra into a 2? 2 matrix Lie algebra. Finally, we discuss the elliptic variable solutions of a generalized BK equation. 相似文献