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NEW ALGEBRAS USING ADDITIVE ABELIAN GROUPS I
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  • Journal title : Honam Mathematical Journal
  • Volume 31, Issue 3,  2009, pp.407-419
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2009.31.3.407
 Title & Authors
NEW ALGEBRAS USING ADDITIVE ABELIAN GROUPS I
Choi, Seul-Hee;
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 Abstract
The simple non-associative algebra and its simple sub-algebras are defined in the papers [1], [3], [4], [5], [6], [12]. We define the non-associative algebra and its antisymmetrized algebra . We also prove that the algebras are simple in this work. There are various papers on finding all the derivations of an associative algebra, a Lie algebra, and a non-associative algebra (see [3], [5], [6], [9], [12], [14], [15]). We also find all the derivations of te antisymmetrized algebra and every derivation of the algebra is outer in this paper.
 Keywords
simple;stable algebra;antisymmetrized algebra;abelian;derivation;
 Language
English
 Cited by
1.
A GROWING ALGEBRA CONTAINING THE POLYNOMIAL RING,;

호남수학학술지, 2010. vol.32. 3, pp.467-480 crossref(new window)
2.
NOTES ON AN ALGEBRA WITH SCALAR DERIVATIONS,;

호남수학학술지, 2014. vol.36. 1, pp.179-186 crossref(new window)
1.
NOTES ON AN ALGEBRA WITH SCALAR DERIVATIONS, Honam Mathematical Journal, 2014, 36, 1, 179  crossref(new windwow)
2.
A GROWING ALGEBRA CONTAINING THE POLYNOMIAL RING, Honam Mathematical Journal, 2010, 32, 3, 467  crossref(new windwow)
 References
1.
Mohammad H. Ahmadi, Ki-Bong Nam. and Jonathan Pakianathan, Lie admissible non-associative algebras, Algebra Colloquium, Vol. 12, No. 1, World Scientific, (March) 2005, 113-120. crossref(new window)

2.
G. Brown, Properties of a 29-dimensional simple Lie algebra of characteristic three, Math. Ann., 261 (1982), no. 4, 487-492. crossref(new window)

3.
Seul Hee Choi and Ki-Bong Nem. The Derivation of a Restricted Weyl Type Non-Associative Algebra, Vol. 28. No.3, Hadronic Journal, 2005, 287-295.

4.
Seul Hee Choi, An algebra with right identities and its antisymmetrized algebra, Honam Mathematical Journal, Vol. 29, No. 2, 2007, 213-222. crossref(new window)

5.
Seul Hee Choi and Ki-Bong Nam, "Weyl type non-associative algebra using additive groups I," Algebra Colloquium, Volume 14 (2007), 479-488, Number 3, 2007. crossref(new window)

6.
Seul Hee Choi and Ki-Bong Nam, "Derivations of a restricted Weyl Type Algebra I", Rocky Mountain Math. Journals, Volume 37, Number 6, 2007. 67-84. crossref(new window)

7.
Seul Hee Choi, Jongwoo Lee, and Ki-Bong Nam, "Derivations of a restricted Weyl type algebra containing the polynomial ring", Communication in Algebra, Volume 36, Issue 9 September 2008, 3435-3446. crossref(new window)

8.
I. N. Herstein, Non commutative Rings, Cams Mathematical Monographs, Mathematical Association of America, 100-101.

9.
T. Ikeda, N. Kawamoto and Ki-Bong Nam, A class of simple subalgebras of Generalized W algebras, Proceedings of the International Conference in 1998 at Pusan (Eds. A. C. Kim), Walter de Gruyter Gmbh Co. KG, 2000, 189-202.

10.
V. G. Kac, Description of Filtered Lie Algebra with which Graded Lie algebras of Cartan type ere Associated, Izv. Akad. Nauk SSSR, Ser. Mat. Tom, 38, 1974, 832-834.

11.
Naoki Kawamoto, Atsushi Mitsukawa, Ki-Bong Nam, and Moon-Ok Wang, The automorphisms of generalize d Witt type Lie algebras, Journal of Lie Theory, 13 Vol(2), Heldermann Verlag, 2003, 571-576.

12.
Jongwoo Lee and Ki-bong Nam, "Non-Associative Algebras containing the Matrix Ring", Linear Algebra and its Applications Volume 429, Issue 1, 1 July 2008, Pages 72-78. crossref(new window)

13.
Ki-Bong Nam, Generalized Wand H Type Lie Algebras, Algebra Colloquium 6:3, (1999), 329-340.

14.
Ki-Bong Nam. On Some Non-Associative Algebras Using Additive Groups, Southeast Asian Bulletin of Mathematics, Vol. 27, Springer Verlag, 2003, 493-500.

15.
Ki-Bong Nam and Moon-Ok Wang, Notes on Some Non-Associative Algebras, Journal of Applied Algebra and Discrete Structured, Vol 1, No, 3, 159-164.

16.
D. P. Passman, Simple Lie algebras of Witt type, J. Algebra 206 (1998).

17.
A. N. Rudakov, Groups of Automorphisms of Infinite-Dimensional Simple Lie Algebras. Math. USSR-Izvestija, 3, 1969, 707-722. crossref(new window)

18.
R. D. Schafer, Introduction to nonassociative algebras, Dover, 1995, 128-138.