AN EXTENDED NON-ASSOCIATIVE ALGEBRA

• Journal title : Honam Mathematical Journal
• Volume 29, Issue 2,  2007, pp.213-222
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2007.29.2.213
Title & Authors
AN EXTENDED NON-ASSOCIATIVE ALGEBRA
Choi, Seul-Hee;

Abstract
A Weyl type algebra is defined in the paper (see [2],[4], [6], [7]). A Weyl type non-associative algebra $\small{\bar{WN_{m,n,s}}}$ and its restricted subalgebra $\small{\bar{WN_{m,n,s_r}}}$ are defined in the papers (see [1], [14], [16]). Several authors find all the derivations of an associative (Lie or non-associative) algebra (see [3], [1], [5], [7], [10], [16]). We find Der($\small{\bar_{WN_{0,0,1_n}}}$) of the algebra $\small{\bar_{WN_{0,0,1_n}}}$ and show that the algebras $\small{\bar_{WN_{0,0,1_n}}}$ and $\small{\bar_{WN_{0,0,s_1}}}$ are not isomorphic in this work. We show that the associator of $\small{\bar_{WN_{0,0,1_n}}}$ is zero.
Keywords
Simple;non-associative algebra;right identity;annihilator;idempotent;
Language
English
Cited by
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2.
DERIVATIONS OF A COMBINATORIAL LIE ALGEBRA,;

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1.
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2.
DERIVATIONS OF A COMBINATORIAL LIE ALGEBRA, Honam Mathematical Journal, 2014, 36, 3, 493
3.
NEW ALGEBRAS USING ADDITIVE ABELIAN GROUPS I, Honam Mathematical Journal, 2009, 31, 3, 407
References
1.
Mohammad H. Ahmadi, Ki-Bong Nam, and Jonathan Pakinathan, Lie admissible non-associative algebras, Algebra Colloquium, Vol. 12, No. 1, World Scientific, March, 2005, 113-120.

2.
Seul Hee Choi, Derivations of a restricted Weyl Type Algebra on a Laurent Extension, Comm. of KMS, Vol. 21, No. 2, 2006.

3.
Seul Hee Choi, Notes on a non-associative algebras with Exponential functions I, Honam Mathematical Journal, Vol. 28, No. 2, 2006.

4.
Seul Hee Choi, Derivations of a Weyl type non-associative algebra on a Laurent extension, Bull. Korean Math. Soc, Vol. 43, No. 3, 2006.

5.
Seul Hee Choi and Ki-Bong Nam, The Derivation of a Restricted Weyl Type Non-Associative Algebra, Vol. 28, No. 3, Hadronic Journal, 2005, 287-295.

6.
Seul Hee Choi and Ki-Bong Nam, Derivations of a restricted Weyl Type Algebra I, Accepted, Rocky Mountain Journal of Mathematics, 2005.

7.
J. Diximier, Enveloping Algebras, AMS, 1996.

8.
J. E. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer-Verlag, New York, 1987, 7-21.

9.
V. G. Kac, Description of Filtered Lie Algebra with which Graded Lie algebras of Cartan type are Associated, Izv. Akad. Nauk SSSR, Ser. Mat. Tom, 38, 1974, 832-834.

10.
T. Ikeda, N. Kawamoto, K. Nam, A class of simple subalgebras of generalized Witt algebras, Groups-Korea '98 (Pusan), de Gruyter, Berlin, 2000, 189-202, MR1751094.

11.
Heejung Jang, A Weyl-Type Non-Associative Algebra with one variable, M.A. Thesis, Jeonju University, 2007.

12.
A. I. Kostrikin and I. R. Safarevic, Graded Lie algebras of finite characteristic, Math. USSR Izv., 3, No. 2, 1970, 237-240.

13.
Ki-Bong Nam, Generalized W and H type Lie Algebras, Algebra Colloquium, Springer Verlag, 1999, 329-340, MR 1809652.

14.
Ki-Bong Nam, Graded radical W-type Lie Algebras I, Internatinal Journal of Mathematics and Mathematical Sciences, Vol. 31 (6) (2002), MR 1927827.

15.
Ki-Suk Lee and Ki-Bong Nam, Some W-type algebras I, J. Appl. Algebra Discrete Struct. 2, No.l, 2004, 39-46, Zbl 1045.17015.

16.
Ki-Bong Nam and Seul Hee Choi, Automorphism group of non-associative algebras $WN_{2,0,01}$, Vol. 1, No. 1, Journal of Computational Mathematics and Opti­mization, SAS publishers, 2005, 35-44.

17.
R. D.Schafer, Introduction to nonassociative algebras, Dover, 1995, 128-138.