Results 211 to 220 of about 361,283 (249)

Affine Lie Algebras

1997
This chapter is a basic introduction to affine Lie algebras, preparing the stage for their application to conformal field theory. In Sect. 14.1.1, after having introduced the affine Lie algebras per se, we show how the fundamental concepts of roots, weights, Cartan matrices, and Weyl groups are extended to the affine case.
Philippe Di Francesco, Pierre Mathieu, David Sénéchal   +2 more
openaire   +2 more sources

FEIGIN-FUCHS REPRESENTATIONS OF $A ^{(1)} _n$ AFFINE LIE ALGEBRA AND THE ASSOCIATED PARAFERMIONIC ALGEBRA

, 1990
In this paper, Feigin-Fuchs representations A{sup (1)}{sub n} affine Lie algebra and the associated parafermionic algebra are obtained. The screening charges, essential for analyzing the structure of irreducible modules, are also discussed.
K. Ito, Y. Kazama
semanticscholar   +1 more source

A non-recursive criterion for weights of a highest-weight module for an affine Lie algebra

, 2010
Let Λ be a dominant integral weight of level k for the affine Lie algebra g and let α be a non-negative integral combination of simple roots. We address the question of whether the weight η = Λ − α lies in the set P(Λ) of weights in the irreducible ...
O. Barshevsky, M. Fayers, M. Schaps
semanticscholar   +1 more source

Structure of the level two Standard Modules for the affine Lie algebra

, 1990
In this paper, we find bases of level two standard modules for the affine Lie algebra using the z—algebra theory developed in [2] by Lepowsky and Wilson. The terms and natations used in this paper can be found in [2].
C. Xie
semanticscholar   +1 more source

Realization of Vertex Operators of 7-Twisted Affine Lie Algebra

, 2010
In this paper, we construct a new algebra structure 7-twisted affine Lie algebra and study its vertex operator representations.
Zheng Zhu-jun, Dong Wen-feng, Chu Yan-jun   +2 more
semanticscholar   +1 more source

A class of irreducible modules for the extended affine Lie algebra

, 2009
We construct a class of modules for extended affine Lie algebra by using the free fields. A necessary and sufficient condition is given for those modules being irreducible.
Ziting Zeng
semanticscholar   +1 more source

AFFINE MODULAR LIE ALGEBRAS

Mathematics of the USSR-Sbornik, 1991
The paper is devoted to the construction of affine Kac-Moody algebras via defining relations arising from an integral affine Cartan matrix, in the case where the ground field has positive characteristic p > 7. Explicit constructions are given for algebras obtained in this way; in distinction with the zero characteristic case they have infinite ...
openaire   +2 more sources

Lie Algebras of Pro-Affine Algebraic Groups

Canadian Journal of Mathematics, 2002
AbstractWe extend the basic theory of Lie algebras of affine algebraic groups to the case of pro-affine algebraic groups over an algebraically closed fieldKof characteristic 0. However, some modifications are needed in some extensions. So we introduce the pro-discrete topology on the Lie algebra ℒ(G) of the pro-affine algebraic groupGoverK, which is ...
openaire   +2 more sources

Affine Lie algebras and vertex operator algebras

1993
In this chapter we shall discuss standard (or integrable highest weight) representations of affine Kac-Moody algebras from the point of view of vertex operator algebra theory. This will also provide the setting for the next chapter. We restrict our attention to a simple Lie algebra G of type A, D or E.
Chongying Dong, James Lepowsky
openaire   +2 more sources

New Irreducible Components of the Space of Foliations Associated to the Affine Lie Algebra

, 2017
R. Lizarbe
semanticscholar   +1 more source