GAMMA-CONFORMAL ALGEBRAS

Gamma-conformal algebra is an axiomatic description of the operator pr oduct expansion of chiral fields with simple poles at finitely many po ints. We classify these algebras and their representations in terms of Lie algebras and their representations with an action of the group Ga mma. To every Gamma-conformal algebra and a character of Gamma we asso ciate 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'' analogue of the general linear algebra ) and its analogues, the algebra of pseudodifferential operators on th e circle, etc. (C) 1998 American Institute of Physics. [S0022-2488(98) 00904-9].