THE GENERALIZED WITT ALGEBRAS USING ADDITIVE MAPS I

  • Nam, Ki-Bong (Department of mathematics, University of wisconsin)
  • Published : 1999.05.01

Abstract

Kawamoto generalized the Witt algebra using F[${X_1}^{\pm1},....{X_n}^{\pm1}$] instead of F[x1,…, xn]. We construct the generalized Witt algebra $W_{g,h,n}$ by using additive mappings g, h from a set of integers into a field F of characteristic zero. We show that the Lie algebra $W_{g,h,n}$ is simple if a g and h are injective, and also the Lie algebra $W_{g,h,n}$ has no ad-digonalizable elements.

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