# 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} }

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…

## 37 Citations

Cohomology of Conformal Algebras

- Mathematics
- 1999

Abstract:The notion of a conformal algebra encodes an axiomatic description of the operator product expansion of chiral fields in conformal field theory. On the other hand, it is an adequate tool for…

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We study Γ-conformal algebras which are a discrete analog of conformal algebras in the sense of V. G. Kac. For a torsion-free group Γ, simple and semisimple associative Γ- conformal algebras of…

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We study the algebra of conformal endomorphisms CendG,Gn of a finitely generated free module Mn over the coordinate Hopf algebra H of a linear algebraic group G. It is shown that a conformal…

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- 2001

We give a complete description of the anti-involutions of the algebra DN of N×N-matrix differential operators on the circle, preserving the principal Z gradation. We obtain, up to conjugation, two…

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- 2001

Conformal algebras, recently introduced by Kac, encode an axiomatic description of the singular part of the operator product expansion in conformal field theory. The objective of this paper is to…

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