(r,s)-微分算子代数的导子及其二上圈(英文)

Derivations and 2-cocycles of the algebra of(r,s)-differential operators

定义复数域■上的Laurent多项式代数■[t,t^(-1)]的(r,s)-微分算子■_(r,s).给出该微分算子及{t^(±1}生成的结合代数即(r,s)-微分算子代数的一组基,并在此基础上研究了(r,s)-微分算子代数的导子代数及其非平凡二上圈.

This paper defined the （r,s）-differential operator of the algebra of Laurent poly- nomials over the complex numbers field. Let 79r,8 be the associative algebra generated by {t^±1} and the （r, s）-differential operator, which is called （r, s）-differential operators algebra. In this paper, the derivation algebra of Dr,s and its Lie algebra Dr,s^- were described and all the non-trivial 2-cocycles were determined.