HOMOLOGICAL PROPERTIES OF SKLYANIN ALGEBRAS

To a pair consisting of an elliptic curve and a point on it, Odeskii a nd Feigin associate certain quadratic algebras (''Sklyanin algebras'') , having the Hilbert series of a polynomial algebra. In this paper we show that Sklyanin algebras have good homological properties and we ob tain some information about their so-called linear modules. We also sh ow how the construction by Odeskii and Feigin may be generalized so as to yield other ''Sklyanin-type'' algebras.