DOI QR코드

DOI QR Code

DERIVATIONS OF A WEYL TYPE NON-ASSOCIATIVE ALGEBRA ON A LAURENT EXTENSTION

  • Choi, Seul-Hee (Department of Mathematics, Jeonju University)
  • Published : 2006.08.01

Abstract

A Weyl type algebra is defined in the book ([4]). A Weyl type non-associative algebra $\={WP_{m,n,s}}$ and its restricted sub-algebra $\={WP_{m,n,s_{\gamma}}}$ are defined in various papers ([1], [12], [3], [11]). Several authors 0nd all the derivations of an associative (Lie or non-associative) algebra in the papers ([1], [2], [12], [4], [6], [11]). We find all the non-associative algebra derivations of the non-associative algebra $\={WP_{0,2,0_B}$, where $B=\{{\partial}_0,\;{\partial}_1,\;{\partial}_2,\;{\partial}_{12},\;{\partial}^2_1,\;{\partial}^2_2\}$.

Keywords

simple;non-associative algebra;Kronecker delta;left identity;annihilator;idempotent;Semi-Lie algebra

References

  1. R. Block, On torsion-free abelian groups and Lie algebras, Proc. Amer. Math. Soc. 9 (1958), 613-620
  2. S. H. Choi and K-B. Nam, Derivations of a restricted Weyl type algebra I, Rocky Mountain J. Math., Accepted, 2005
  3. J. Diximier, Enveloping Algebras, AMS, 1996
  4. J. E. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer-Verlag, New York, 1978
  5. T. Ikeda, N. Kawamoto, and K. Nam, A class of simple subalgebras of generalized Witt algebras, Groups-Korea '98 (Pusan), de Gruyter, Berlin, 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. A. I. Kostrikin and I. R. Safarevic, Graded Lie algebras of finite characteristic, Math. USSR Izv. 3 (1970), no. 2, 237-240 https://doi.org/10.1070/IM1969v003n02ABEH000766
  8. K.-S. Lee and K.-B. Nam, Some W-type algebras I, J. Appl. Algebra Discrete Struct. 2 (2004), no. 1, 39-46
  9. K.-B. Nam, Generalized W and H type Lie algebras, Algebra Colloq. 6 (1999), no. 3, 329-340
  10. K.-B. Nam and S. H. Choi, Automorphism group of non-associative algebras $\ba{WN_{2,0,0_1}}$, J. Comput. Math. Optim. 1 (2005), no. 1, 35-44
  11. K.-B. Nam, S. H. Choi, M.-O. Wang, Weyl-type non-associative algebras III, J. Appl. Algebra Discrete Struct. 3 (2005), no. 2, 91-100
  12. H. M. Ahmadi, K.-B. Nam, and J. Pakianathan, Lie admissible non-associative algebras, Algebra Colloq. 12 (2005), no. 1, 113-120 https://doi.org/10.1142/S1005386705000106