超对称自对偶杨─Mills模型的Hamilton约化

本文研究了４维超对称自对偶杨－Ｍｉｌｌｓ模型的Ｈａｍｉｌｔｏｎ约化．在左右对称的常约束下导出了４维超对称非阿贝尔Ｔｏｄａ模型、相应的作用量以及线性系统．在主阶化下的１阶约束条件下，得到了４维超对称Ｔｏｄａ模型．本文的约化对任意李超代数都成立，并不特别要求李超代数具有纯奇素根系．     

The Solution Construction of Heterotic Super-Liouville Model

We investigate the heterotic super-Liouville model on the base of the basic Lie super-algebra Osp(1|2).Using the super extension of Leznov-Saveliev analysis and Drinfeld Sokolov linear system, we construct the explicit solution of the heterotic super-Liouville system in component form. We also show that the solutions are local and periodic by calculating the exchange relation of the solution. Finally starting from the action of heterotic super-Liou ville model, we obtain the conserved current and conserved charge which possessed the BR ST properties.     

The Solution Construction of Heterotic Super-Liouville Model

We investigate the heterotic super-Liouville model on the base of the basic Lie super-algebra Osp(1|2).Using the super extension of Leznov-Saveliev analysis and Drinfeld Sokolov linear system, we construct the explicit solution of the heterotic super-Liouville system in component form. We also show that the solutions are local and periodic by calculating the exchange relation of the solution. Finally starting from the action of heterotic super-Liou ville model, we obtain the conserved current and conserved charge which possessed the BR ST properties.     

Integrable Systems and Two-Dimensional Gravity from Conformally Reduced WZNW Model

Imposing constraints with an integer ordering on WZNW model a large series of conformal invariant integrable systems will result. In this letter, a general approach for imposing the first and the second class constraints based on an arbitrary grading scheme of the Lie algebras of the WZNW groups is presented. The first order constraints correspond to integrable systems containing super Toda and conformal affine Toda systems as examples and are related to two-dimensional induced gravity, whilst the second order constraints correspond to supersymmetric-like integrable systems containing super Toda and conformal affine super Toda systems (for super WZNW groups) and are conjectured to be related to twodimensional induced supergravity.     

Expansions of Algebras and Superalgebras and Some Applications

After reviewing the three well-known methods to obtain Lie algebras and superalgebras from given ones, namely, contractions, deformations and extensions, we describe a fourth method recently introduced, the expansion of Lie (super)algebras. Expanded (super)algebras have, in general, larger dimensions than the original algebra, but also include the ?nönü–Wigner and generalized IW contractions as a particular case. As an example of a physical application of expansions, we discuss the relation between the possible underlying gauge symmetry of eleven-dimensional supergravity and the superalgebra osp(1|32).     

The gl (M|N) super Yangian and its finite-dimensional representations

Methods are developed for systematically constructing the finite-dimensional irreducible representations of the super Yangian Y (gl(M|N)) associated with the Lie superalgebra gl(M|N). It is also shown that every finite-dimensional irreducible representation of Y (gl(M|N)) is of highest weight type, and is uniquely characterized by a highest weight. The necessary and sufficient conditions for an irrep to be finite-dimensional are given.     

Integrable Highest Weight Modules over Affine Superalgebras and Appell's Function

We classify integrable irreducible highest weight representations of non-twisted affine Lie superalgebras. We give a free field construction in the level 1 case. The analysis of this construction shows, in particular, that in the simplest case of the sℓ (2|1) level 1 affine superalgebra the characters are expressed in terms of the Appell elliptic function. Our results demonstrate that the representation theory of affine Lie superalgebras is quite different from that of affine Lie algebras. Received: 17 April 2000 / Accepted: 7 July 2000     

W-algebras and superalgebras from constrained WZW models: A group theoretical classification

We present a classification ofW algebras and superalgebras arising in Abelian as well as non Abelian Toda theories. Each model, obtained from a constrained WZW action, is related with anSl(2) subalgebra (resp.OSp(1/2) superalgebra) of a simple Lie algebra (resp. superalgebra)G. However, the determination of anU(1) _Y factor, commuting withSl(2) (resp.OSp(1/2)), appears, when it exists, particularly useful to characterize the correspondingW algebra. The (super) conformal spin contents of eachW (super) algebra is performed. The class of all the superconformal algebras (i.e. with conformal spinss<=2) is easily obtained as a byproduct of our general results.     

Quantum Affine Superalgebra Uq(gl(1|1)) and Its

Drinfeld's realization of quantum affine superalgebra U_q(gl(1|1)) is given based on the super version of RS construction method and Gauss decomposition.     

Strings fromN=2 gauged Wess-Zumino-Witten models

We present an algebraic approach to string theory. An embedding ofsl(2|1) in a super Lie algebra together with a grading on the Lie algebra determines a nilpotent subalgebra of the super Lie algebra. Chirally gauging this subalgebra in the corresponding Wess-Zumino-Witten model, breaks the affine symmetry of the Wess-Zumino-Witten model to some extension of theN=2 superconformal algebra. The extension is completely determined by thesl(2|1) embedding. The realization of the superconformal algebra is determined by the grading. For a particular choice of grading, one obtains in this way, after twisting, the BRST structure of a string theory. We classify all embeddings ofsl(2|1) into Lie super algebras and give a detailed account of the branching of the adjoint representation. This provides an exhaustive classification and characterization of both all extendedN=2 superconformal algebras and all string theories which can be obtained in this way.     

THE FIRST COHOMOLOGY OF THE SUPERCONFORMAL ALGEBRA K(1|4)

The infinitesimal deformations of the embedding of the Lie superalgebra of contact vector fields on the supercircle S^1|4 into the Poisson superalgebra of symbols of pseudodifferential operators on S^1|2 are explicitly calculated.     

On Two-Parameter Deformations of osp(1|2)(1)

An elliptic two-parameter deformation of the (universal enveloping superalgebra of) affine Lie superalgebra osp(1|2)⁽¹⁾ is proposed in terms of free boson realization. This deformed superalgebra is shown to fit in the framework of infinite Hopf family of superalgebras, a generalization of the infinite Hopf family of algebras proposed earlier by the authors. The trigonometric and rational degenerations are briefly discussed.     

Integrable graded manifolds and nonlinear equations

A method is proposed for the classification of integrable embeddings of (2+2)-dimensional supermanifoldsV _2|2 into an enveloping superspace supplied with the structure of a Lie superalgebra. The approach is first applied to the even part of the scheme, i.e. for the embeddings of 2-dimensional manifoldsV ₂ into Riemannian or non-Riemannian enveloping space. The general consideration is also illustrated by the example of superspaces supplied with the structure of the series sl(n, n+1), whose integrable supermanifolds are described by supersymmetrical 2-dimensional Toda lattice type equations. In particular, forn=1 they are described by the supersymmetrical Liouville and Sine-Gordon equations.     

Lie Algebras and Superalgebras Defined by a Finite Number of Relations: Computer Analysis

Abstract

The presentation of Lie (super)algebras by a finite set of generators and defining relations is one of the most general mathematical and algorithmic schemes of their analysis. It is very important, for instance, for investigation of the particular Lie (super)algebras arising in different (super)symmetric physical models. Generally, one can put the following question: what is the most general Lie algebra or superalgebra satisfying to the given set of Lie polynomial equations? To solve this problem, one has to perform a large volume of algebraic transformations which sharply increases with growth of the number of generators and relations. By this reason, in practice, one needs to use a computer algebra tool. We describe here an algorithm and its implementation in C for constructing the bases of finitely presented Lie (super)algebras and their commutator tables.     

Cyclic Representations of Quantum (Super) Algebras At qp=1

Cyclic representations of quantum (super) algebras are studied at q^p=1 using two methods:the quotient module method and the q-boson realization method.For the quantum algebras associated with any finite dimensional simple Lie algebra the general theory of two methods is given,and is generated to the quantum superalgebra U_qosp(1.2).By constructing the cyclic representation of q-Heisenberg-Wey1 superalgebras the q-boson realization method is generated to construction of cyclic representations of some high-rank quantum superalgebras.     

Parabosons,parafermions, and explicit representations of infinite-dimensional algebras

The goal of this paper is to give an explicit construction of the Fock spaces of the parafermion and the paraboson algebra, for an infinite set of generators. This is equivalent to constructing certain unitary irreducible lowest weight representations of the (infinite rank) Lie algebra so(∞) and of the Lie superalgebra osp(1|∞). A complete solution to the problem is presented, in which the Fock spaces have basis vectors labeled by certain infinite but stable Gelfand-Zetlin patterns, and the transformation of the basis is given explicitly. Alternatively, the basis vectors can be expressed as semi-standard Young tableaux.     

Generalized Toda Mechanics Associated with Loop Algebras (L)(Cr) and (L)(Dr) and Their Reductions

We construct a class of integrable generalization of Toda mechanics with long-range interactions. These systems are associated with the loop algebras L(C_r) and L(D_r) in the sense that their Lax matrices can be realized in terms of the c=0 representations of the affine Lie algebras C⁽¹⁾_r and D⁽¹⁾_r and the interactions pattern involved bears the typical characters of the corresponding root systems. We present the equations of motion and the Hamiltonian structure. These generalized systems can be identified unambiguously by specifying the underlying loop algebra together with an ordered pair of integers (n,m). It turns out that different systems associated with the same underlying loop algebra but with different pairs of integers (n₁,m₁) and (n₂,m₂) with n₂<n₁ and m₂<m₁ can be related by a nested Hamiltonian reduction procedure. For all nontrivial generalizations, the extra coordinates besides the standard Toda variables are Poisson non-commute, and when either $n$ or m≥3, the Poisson structure for the extra coordinate variables becomes some Lie algebra (i.e. the extra variables appear linearly on the right-hand side of the Poisson brackets). In the quantum case, such generalizations will become systems with noncommutative variables without spoiling the integrability.     

En">The Second Cohomology of sl ( m | 1 ) with Coefficients in its Enveloping Algebra is Trivial

Using techniques developed in a recent article by the authors, it is proved that the 2-cohomology of the Lie superalgebra sl ( m | 1 ) m 2, with coefficients in its enveloping algebra is trivial. The obstacles in solving the analogous problem for sl ( 3 | 2 ) are also discussed.     

Solutions of super Knizhnik–Zamolodchikov equations

Letters in Mathematical Physics - We establish an explicit bijection between the sets of singular solutions of the (super) KZ equations associated with the Lie superalgebra, of infinite rank, of...