• Published : 2007.05.31


For the evaluation algebra $F[e^{{\pm}x}]_M\;if\;M=\{{\partial}\}$, then $$Der_{non}(F[e^{{\pm}x}]_M)$$ of the evaluation algebra $(F[e^{{\pm}x}]_M)$ is found in the paper [15]. For $M=\{{\partial},\;{\partial}^2\}$, we find $Der_{non}(F[e^{{\pm}x}]_M))$ of the evaluation algebra $F[e^{{\pm}x}]_M$ in this paper. We show that there is a non-associative algebra which is the direct sum of derivation invariant subspaces.


simple;Witt algebra;graded;radical homogeneous equivalent component;order;derivation invariant


  1. M. H. Ahmadi, K. B. Nam, and J. Pakinathan, Lie admissible non-associative algebras, Algebra Colloq. 12 (2005), no. 1, 113-120
  2. S. H. Choi and K. B. Nam, The derivation of a restricted Weyl type non-associative algebra, Hadronic J. 28 (2005), no. 3, 287-295
  3. S. H. Choi, Derivation of symmetric non-associative algebra I, Algebras Groups Geom. 22(2005), no. 3, 341-352
  4. S. H. Choi, Derivations of a restricted Weyl type algebra I, Accepted, Rocky Mountain Journal of Mathematics, 2005
  5. V. G. Kac, Description of filtered Lie algebra with which graded Lie algebras of Cartan type are associated, Izv. Akad. Nauk SSSR Ser. Mat. 38 (1974), 800-834
  6. N. Kawamoto, A. Mitsukawa, K. B. Nam, and M. O. Wang, The automorphisms of generalized Witt type Lie algebras, J. Lie Theory 13 (2003), no. 2, 573-578
  7. I. Kaplansky, The Virasoro algebra, Comm. Math. Phys. 86 (1982), no. 1, 49-54
  8. K. B. Nam, On some non-associative algebras using additive groups, Southeast Asian Bull. Math. 27 (2003), no. 3, 493-500
  9. K. B. Nam and S. H. Choi, On the derivations of non-associative Weyl-type algebras, Appear, Southeast Asian Bull. Math., 2005
  10. K. B. Nam, Y. Kim, and M. O. Wang, Weyl-type non-associative algebras I, Advances in algebra towards millenninum problems, SAS Publishers (2005), 147-155
  11. K. B. Nam and M. O. Wang, Notes on some non-associative algebras, J. Appl. Algebra Discrete Struct. 1 (2003), no. 3, 159-164
  12. R. D. Schafer, Introduction to nonassociative algebras, Dover, 1995
  13. M. O. Wang, J. G. Hwang, and K. S. Lee, Some results on non-associative algebras, Bull. Korean Math. Soc., Accepted, 2006
  14. T. Ikeda, N. Kawamoto, and K. B. Nam, A class of simple subalgebras of Generalized Witt algebras, Proceedings of the International Conference in 1998 at Pusan (Eds. A. C. Kim), Walter de Gruyter Gmbh Co. KG (2000), 189-202
  15. A. N. Rudakov, Groups of automorphisms of infinite-dimensional simple Lie algebras, Math. USSR-Izv. 3 (1969), 707-722

Cited by

  1. Non-associative Algebras with n-Exponential Functions vol.16, pp.01, 2009,