Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

NOTES ON A NON-ASSOCIATIVE ALGEBRA WITH EXPONENTIAL FUNCTIONS II

  • Published : 2007.05.31
Download PDF
⟨ Previous Next ⟩

Abstract

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.

Keywords

References

  1. M. H. Ahmadi, K. B. Nam, and J. Pakinathan, Lie admissible non-associative algebras, Algebra Colloq. 12 (2005), no. 1, 113-120 https://doi.org/10.1142/S1005386705000106
  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. 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
  6. 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
  7. 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
  8. I. Kaplansky, The Virasoro algebra, Comm. Math. Phys. 86 (1982), no. 1, 49-54 https://doi.org/10.1007/BF01205660
  9. K. B. Nam, On some non-associative algebras using additive groups, Southeast Asian Bull. Math. 27 (2003), no. 3, 493-500
  10. K. B. Nam and S. H. Choi, On the derivations of non-associative Weyl-type algebras, Appear, Southeast Asian Bull. Math., 2005
  11. 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
  12. K. B. Nam and M. O. Wang, Notes on some non-associative algebras, J. Appl. Algebra Discrete Struct. 1 (2003), no. 3, 159-164
  13. A. N. Rudakov, Groups of automorphisms of infinite-dimensional simple Lie algebras, Math. USSR-Izv. 3 (1969), 707-722 https://doi.org/10.1070/IM1969v003n04ABEH000798
  14. R. D. Schafer, Introduction to nonassociative algebras, Dover, 1995
  15. M. O. Wang, J. G. Hwang, and K. S. Lee, Some results on non-associative algebras, Bull. Korean Math. Soc., Accepted, 2006 https://doi.org/10.4134/BKMS.2007.44.1.095

Cited by

  1. Non-associative Algebras with n-Exponential Functions vol.16, pp.01, 2009, https://doi.org/10.1142/S1005386709000108