华东师范大学学报(自然科学版) ›› 2009, Vol. 2009 ›› Issue (1): 94-103.

• 应用数学与基础数学 • 上一篇    下一篇

(r,s)-微分算子代数的导子及其二上圈(英文)

陈茹1, 林磊1, 刘东2   

  1. 1.华东师范大学 数学系, 上海 200062; 2.湖州师范学院 数学系, 浙江 湖州 313000
  • 收稿日期:2008-04-21 修回日期:2008-05-30 出版日期:2009-01-25 发布日期:2009-01-25

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

CHEN Ru1, LIN Lei1, LIU Dong2   

  1. 1.Department of Mathematics, East China Normal University, Shanghai 200062, China;2.Department of Mathematics, Huzhou Teachers College, Huzhou Zhejiang 233041, China
  • Received:2008-04-21 Revised:2008-05-30 Online:2009-01-25 Published:2009-01-25

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摘要：

定义复数域\,$\c$\,上的\,Laurent\,多项式代数\,$\c[t,t^{-1}]$~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.

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

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