# Γ-conformal algebras

@article{GolenishchevaKutuzova1998conformalA,
title={$\Gamma$-conformal algebras},
author={Maria I. Golenishcheva-Kutuzova and Victor G. Kac},
journal={Journal of Mathematical Physics},
year={1998},
volume={39},
pages={2290-2305}
}
• Published 1 September 1997
• Mathematics
• Journal of Mathematical Physics
Γ-conformal algebra is an axiomatic description of the operator product expansion of chiral fields with simple poles at finitely many points. We classify these algebras and their representations in terms of Lie algebras and their representations with an action of the group Γ. To every Γ-conformal algebra and a character of Γ we associate a Lie algebra generated by fields with the OPE with simple poles. Examples include twisted affine Kac–Moody algebras, the sin algebra (which is a “Γ-conformal…
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## References

SHOWING 1-10 OF 14 REFERENCES
P ALGEBRA OF KP, FREE FERMIONS AND 2-COCYCLE IN THE LIE ALGEBRA OF PSEUDODIFFERENTIAL OPERATORS
• Mathematics
• 1997
The symmetry algebra P∞=W∞⊕ H ⊕ I∞ of integrable systems is defined. As an example the classical Sophus Lie point symmetries of all higher KP equations are obtained. It is shown that one ("positive")
Vertex representations of quantum affine algebras.
• Mathematics
Proceedings of the National Academy of Sciences of the United States of America
• 1988
In the case of the quantum affine algebra of type A, this work introduces vertex operators corresponding to all the roots and determine their commutation relations, which provides an analogue of a Chevalley basis of the affine Lie algebra [unk](n) in the basic representation.
Extensions and contractions of the Lie algebra of q-pseudodifferential symbols
• Mathematics
• 1994
We construct cocycles on the Lie algebra of pseudo- and q-pseudodifferential symbols of one variable and on their close relatives: the sine-algebra and the Poisson algebra on two-torus. A quantum''
Poisson-Lie group of pseudodifferential symbols
• Mathematics
• 1993
We introduce a Lie bialgebra structure on the central extension of the Lie algebra of differential operators (with scalar or matrix coefficients) on the line and on the circle. This defines a
Vertex operator representation of some quantum tori Lie algebras
• Mathematics
• 1992
AbstractWe are defining the trigonometric Lie subalgebras in $$\bar X_\infty = \bar A_\infty (\bar B_\infty ,\bar C_\infty ,\bar D_\infty )$$ which are the natural generalization of the well known
Vertex algebras for beginners
Preface. 1: Wightman axioms and vertex algebras. 1.1: Wightman axioms of a QFT. 1.2: d = 2 QFT and chiral algebras. 1.3: Definition of a vertex algebra. 1.4: Holomorphic vertex algebras. 2: Calculus
The idea of locality
This is a review of recent results on conformal (super)algebras. It may be viewed as an amplification of my Wigner medal acceptance speech (given in July 1996 in Goslar, Germany) reproduced in the
The idea of locality Physial applications and mathematical aspects of geometry, groups and algebras
• Doebner et al editors
• 1997