关键词: (r, s)-微分算子, 导子, 二上圈, (r, s)-微分算子, 导子, 二上圈

Abstract:

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.

Key words: s)-differential operator, Derivation, 2-cocycle, (r, s)-differential operator, Derivation, 2-cocycle