• 제목/요약/키워드: non-associative algebra

검색결과 20건 처리시간 0.021초

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

  • Choi, Seul-Hee
    • 대한수학회보
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    • 제43권3호
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    • pp.627-634
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    • 2006
  • 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 $B=\{{\partial}_0,\;{\partial}_1,\;{\partial}_2,\;{\partial}_{12},\;{\partial}^2_1,\;{\partial}^2_2\}$.

DERIVATIONS OF A RESTRICTED WEYL TYPE ALGEBRA ON A LAURENT EXTENSION

  • Choi Seul-Hee
    • 대한수학회논문집
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    • 제21권2호
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    • pp.227-236
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    • 2006
  • Several authors find all the derivations of an algebra [1], [3], [7]. A Weyl type non-associative algebra and its sub algebra are defined in the paper [2], [3], [10]. All the derivations of the non-associative algebra $\overline{WN_{0,0,s1}$ is found in this paper [4]. We find all the derivations of the non-associative algebra $\overline{WN_{0,s,01}$ in this paper [5].

NOTES ON ${\overline{WN_{n,0,0_{[2]}}}$ I

  • CHOI, SEUL HEE
    • 호남수학학술지
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    • 제27권4호
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    • pp.571-581
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    • 2005
  • The Weyl-type non-associative algebra ${\overline{WN_{g_n,m,s_r}}$ and its subalgebra ${\overline{WN_{n,m,s_r}}$ are defined and studied in the papers [8], [9], [10], [12]. We will prove that the Weyl-type non-associative algebra ${\overline{WN_{n,0,0_{[2]}}}$ and its corresponding semi-Lie algebra are simple. We find the non-associative algebra automorphism group $Aut_{non}({\overline{WN_{1,0,0_{[2]}}})$.

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NOTES ON AN ALGEBRA WITH SCALAR DERIVATIONS

  • Choi, Seul Hee
    • 호남수학학술지
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    • 제36권1호
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    • pp.179-186
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    • 2014
  • In this paper, we consider the simple non-associative algebra $\overline{WN(\mathbb{F}[e^{{\pm}x^r},0,1]_{(\partial,\partial^2)})}$. There are many papers on finding the derivations of an associative algebra, a Lie algebra, and a non-associative algebra (see [2], [3], [4], [5], [6], [7], [12], [14]). We find all the derivations of the algebra $\overline{WN(\mathbb{F}[e^{{\pm}x^r},0,1]_{(\partial,\partial^2)})}$.

DERIVATIONS OF A NON-ASSOCIATIVE GROWING ALGEBRA

  • Choi, Seul Hee
    • 호남수학학술지
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    • 제40권2호
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    • pp.227-237
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    • 2018
  • There are various papers on finding all the derivations of a non-associative algebra and an anti-symmetrized algebra. We find all the derivations of a growing algebra in the paper. The dimension of derivations of the growing algebra is one and every derivation of the growing algebra is outer. We show that there is a class of purely outer algebras in this work.

AN EXTENDED NON-ASSOCIATIVE ALGEBRA

  • Choi, Seul-Hee
    • 호남수학학술지
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    • 제29권2호
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    • pp.213-222
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    • 2007
  • A Weyl type algebra is defined in the paper (see [2],[4], [6], [7]). A Weyl type non-associative algebra $\bar{WN_{m,n,s}}$ and its restricted subalgebra $\bar{WN_{m,n,s_r}}$ 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($\bar_{WN_{0,0,1_n}}$) of the algebra $\bar_{WN_{0,0,1_n}}$ and show that the algebras $\bar_{WN_{0,0,1_n}}$ and $\bar_{WN_{0,0,s_1}}$ are not isomorphic in this work. We show that the associator of $\bar_{WN_{0,0,1_n}}$ is zero.

DERIVATIONS OF A COMBINATORIAL LIE ALGEBRA

  • Choi, Seul Hee
    • 호남수학학술지
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    • 제36권3호
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    • pp.493-503
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    • 2014
  • We consider the simple antisymmetrized algebra $N(e^{A_P},n,t)_1^-$. The simple non-associative algebra and its simple subalgebras are defined in the papers [1], [3], [4], [5], [6], [8], [13]. Some authors found all the derivations of an associative algebra, a Lie algebra, and a non-associative algebra in their papers [2], [3], [5], [7], [9], [10], [13], [15], [16]. We find all the derivations of the Lie subalgebra $N(e^{{\pm}x_1x_2x_3},0,3)_{[1]}{^-}$ of $N(e^{A_p},n,t)_k{^-}$ in this paper.

NEW ALGEBRAS USING ADDITIVE ABELIAN GROUPS I

  • Choi, Seul-Hee
    • 호남수학학술지
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    • 제31권3호
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    • pp.407-419
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    • 2009
  • The simple non-associative algebra $N(e^{A_S},q,n,t)_k$ and its simple sub-algebras are defined in the papers [1], [3], [4], [5], [6], [12]. We define the non-associative algebra $\overline{WN_{(g_n,\mathfrak{U}),m,s_B}}$ and its antisymmetrized algebra $\overline{WN_{(g_n,\mathfrak{U}),m,s_B}}$. 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 $Der_{anti}(WN(e^{{\pm}x^r},0,2)_B^-)$ of te antisymmetrized algebra $WN(e^{{\pm}x^r}0,2)_B^-$ and every derivation of the algebra is outer in this paper.

NOTES ON ${\overline{WN_{n,0,0_{[2]}}}$ II

  • CHOI, SEUL HEE
    • 호남수학학술지
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    • 제27권4호
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    • pp.583-593
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    • 2005
  • The Weyl-type non-associative algebra ${\overline{WN_{g_n,m,s_r}}$ and its subalgebra ${\overline{WN_{n,m,s_r}}$ are defined and studied in the papers [2], [3], [9], [11], [12]. We find the derivation group $Der_{non}({\overline{WN_{1,0,0_{[2]}}})$ the non-associative simple algebra ${\overline{WN_{1,0,0_{[2]}}}$.

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