Journal of East China Normal University(Natural Sc ›› 2009, Vol. 2009 ›› Issue (1): 94-103.

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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


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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