(r,s)-微分算子代数的导子及其二上圈(英文)

定义复数域\,$\c$\,上的\,Laurent\,多项式代数\,$\ct,t^{-1}]$~的\,$(r,s)$-微分算子~$\partial_{r,s}$.~% 给出该微分算子及~$\{ t^{\pm 1}\}$~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.

Derivations and 2-Cocycles of the Algebra of (r,s)-Differential Operators(English)

This paper defined the $(r,s)$-differential operator of the algebra of Laurent polynomials over the complex numbers field. Let $\mathcal{D}_{r,s}$ be the associative algebra generated by $\{ t^{\pm 1} \}$ and the $(r,s)$-differential operator, which is called ($r,s$)-differential operators algebra. In this paper, the derivation algebra of $\mathcal{D}_{r,s}$ and its Lie algebra $\mathcal{D}_{r,s}^-$ were described and all the non-trivial 2-cocycles were determined.