Riemann面上多极点亚纯向量场的代数及其在亚纯λ-微分的实现(Ⅰ)

THE ALGEBRAS OF MEROMORPHIC VECTOR FIELDS AND ITS REALIZATION ON THE SPACES OF MEROMORPHIC λ-DIFFERENTIALS ON RIEMANN SURFACES (Ⅰ)

本文给出球面上亚纯向量场代数的明显构造,并给出这一代数的中心扩充。研究了作为这一代数的实现球面上亚纯λ-微分的性质。

The algebra of meromorphic vector fields with multi-poles on Riemann sphere and the central extension of the algebra are constructed explicitly. Some properties of meromorphic λ- differentials, in particular, of the third kind differentials are investigated.