# 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.

#### References

1. Proc. Amer. Soc. v.9 On torsion-free abelian groups and Lie algebras R. Block
2. Izv. Akad. Nauk SSSR, Ser. Mat. Tom v.38 Descriprion fo Filtered Lie Algebra with which Graded Lie algebras of Cartan type are Associated V. G. Kac
3. Hiroshima Math J. v.16 Generalizations of Witt algebras over a field of characteristic zero N. Kawamoto
4. Contem. Math. A.M.S. v.184 On G-Graded Automorphisms of generalized witt algebras N. Kawamoto
5. UW-Madison, Thesis Generalized Witt algebras over a field of characteristic zero K. Nam
6. Kyungpook Math. J. Accepted Simple Lie algebras which generalize the Witt algebras K. Nam
7. J. of Algebra, to appear Simple Lie algebras of Witt-Type D. S. Passman
8. Math. USSR-Izvestija v.3 Groups of Automorphisms of Infinite-Dimensional Simple Lie Algebras A. N. Rudakov