Ξ-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 Ξ. To every
Ξ-conformal algebra and a character of Ξ 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
``Ξ-conformal'' analodue of the general linear algebra) and its
analogues, the algebra of pseudodifferential operators on the circle, etc.Comment: 23 pages, AMSLatex Repotr-no: ITEP-TH-28/9