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A NOTE ON A WEYL-TYPE ALGEBRA

  • Fernandez, Juan C. Gutierrez (Departamento de Matematica-IME, Universidade de Sao Paulo) ;
  • Garcia, Claudia I. (EACH, Universidade de Sao Paulo)
  • Received : 2015.06.25
  • Accepted : 2016.03.15
  • Published : 2016.06.25

Abstract

In a paper of S. H. Choi [2], the author studied the derivations of a restricted Weyl Type non-associative algebra, and determined a 1-dimensional vector space of derivations. We describe all the derivations of this algebra and prove that they form a 3-dimensional Lie algebra.

Keywords

Non-associative algebra;Lie algebra;derivation

References

  1. H.M. Ahmadi and Ki-Bong Nam, J. Pakinathan, Lie admissible non-associative algebras, Algebra Colloq., 12 (2005), 113-120. https://doi.org/10.1142/S1005386705000106
  2. Seul Hee Choi, Notes on an algebra with scalar derivations, Honam Math. J. 36 (2014), 179-186. https://doi.org/10.5831/HMJ.2014.36.1.179
  3. Seul Hee Choi, Jongwoo Lee and Ki-Bong Nam, Derivations of a restricted Weyl-type algebra containing the polynomial ring, Comm. in Algebra, 36 (2008), 3435-3446. https://doi.org/10.1080/00927870802107835
  4. I. Kaplansky, The first summer mathematical institute, Bull. Amer. Math. Soc., 60 (1954), 457-471. https://doi.org/10.1090/S0002-9904-1954-09832-4
  5. Jongwoo Lee and Ki-Bong Nam, Non-associative algebras containing the matrix ring, Linear Algebra Appl. 429 (2008), 72-78. https://doi.org/10.1016/j.laa.2008.02.005
  6. Ki-Suk Lee and Ki-Bong Nam, Some W-type algebras I, J. Appl. Algebra Discrete Struct., 2 (2004), 39-46.
  7. Ki-Bong Nam, On some non-associative algebras using additive groups, Southeast Asian Bull. Math., 27 (2003), 493-500.
  8. Ki-Bong Nam and Seul Hee Choi, Automorphism group of non-associative algebra ${\overline{WN_{2,0,0_1}}$, J. Comput. Math. and Optim., 1 (2005), 35-44.
  9. Ki-Bong Nam and Seul Hee Choi, On evaluation algebras, Southeast Asian Bull. Math., 29 (2005), 381-385.
  10. J.M. Osborn, New simple infinite-dimensional Lie algebras of characteristic 0, J. Algebra, 185 (1996), 820-835. https://doi.org/10.1006/jabr.1996.0352
  11. D.S. Passman, Simple Lie algebras of Witt type, J. Algebra, 206 (1998), 682-692. https://doi.org/10.1006/jabr.1998.7444