NEW ALGEBRAS USING ADDITIVE ABELIAN GROUPS I

• 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;

Abstract
The simple non-associative algebra $\small{N(e^{A_S},q,n,t)_k}$ and its simple sub-algebras are defined in the papers [1], [3], [4], [5], [6], [12]. We define the non-associative algebra $\small{\overline{WN_{(g_n,\mathfrak{U}),m,s_B}}}$ and its antisymmetrized algebra $\small{\overline{WN_{(g_n,\mathfrak{U}),m,s_B}}}$. 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 $\small{Der_{anti}(WN(e^{{\pm}x^r},0,2)_B^-)}$ of te antisymmetrized algebra $\small{WN(e^{{\pm}x^r}0,2)_B^-}$ 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
2.
NOTES ON AN ALGEBRA WITH SCALAR DERIVATIONS,;

호남수학학술지, 2014. vol.36. 1, pp.179-186
1.
NOTES ON AN ALGEBRA WITH SCALAR DERIVATIONS, Honam Mathematical Journal, 2014, 36, 1, 179
2.
A GROWING ALGEBRA CONTAINING THE POLYNOMIAL RING, Honam Mathematical Journal, 2010, 32, 3, 467
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