$\Gamma$-Conformal Algebras

Abstract

$\Gamma$-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 $\Gamma$. To every $\Gamma$-conformal algebra and a character of $\Gamma$ 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 ``$\Gamma$-conformal'' analodue of the general linear algebra) and its analogues, the algebra of pseudodifferential operators on the circle, etc.

23 pages, AMSLatex Repotr-no: ITEP-TH-28/97

References in corpus (3)

• Poisson-Lie group of pseudodifferential symbols
• Intertwining Operators for the Central Extension of the Yangian Double
• $P_{\infty }$ algebra of KP, free fermions and 2-cocycle in the Lie algebra of pseudodifferential operators

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• An approach to Quantum Conformal Algebra
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• $(G,{\chi }_{\varphi })$-equivariant $\varphi$-coordinated modules for vertex algebras
• On quasi modules at infinity for vertex algebras
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