• Korean Journal of Mathematics
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• v.26 no.1
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• pp.53-60
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• 2018

In this paper, we consider the question of the Rota-Baxter operators of 3-dimensional Heisenberg Lie algebra on ${\mathbb{F}}$, where ${\mathbb{F}}$ is an algebraic closed field. By using the Lie product of the basis elements of Heisenberg Lie algebras, all Rota-Baxter operators of 3-dimensional Heisenberg Lie algebras are calculated and left symmetric algebras of 3-dimensional Heisenberg Lie algebra are determined by using the Yang-Baxter operators.

• Journal of the Korean Mathematical Society
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• v.49 no.2
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• pp.419-433
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• 2012

In this paper, we show that under certain conditions every Lie higher derivation and Lie triple derivation on a triangular algebra are proper, respectively. The main results are then applied to (block) upper triangular matrix algebras and nest algebras.

• Honam Mathematical Journal
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• v.41 no.2
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• pp.369-380
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• 2019

Inspired by the problem of finding hyperelastic curves in a Riemannian manifold, we present a study on the variational problem of a hyperelastic curve in Lie group. In a Riemannian manifold, we reorganize the characterization of the hyperelastic curve with appropriate constraints. By using this equilibrium equation, we derive an Euler-Lagrange equation for the hyperelastic energy functional defined in a Lie group G equipped with bi-invariant Riemannian metric. Then, we give a solution of this equation for a null hyperelastic Lie quadratic when Lie group G is SO(3).

• Cross-Cultural Studies
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• v.29
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• pp.85-111
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• 2012

Zhong-lie-xiao-wu-yi(忠烈小五義), whose author was Shiyukun(石玉昆), is a Xia-Yi-Gong-An(俠義公案) novel in the late Qing Dynasty. This work published in 1890 when Emperor Guangxu(光緖) governed China. This work's author is Shiyukun, distribution books has an amender. The amender will be a shuoshuyiren (說書藝人). Zhong-lie-xiao-wu-yi is Zhong-lie-xia-yi-zhuan(忠烈俠義傳)'s a sequel, the story leads from Zhong-lie-xia-yi-zhuan. It is just the beginning of Zhong-lie-xiao-wu-yi is redundant. Zhong-lie-xiao-wu-yi was introduced to the late Chosun(朝鮮) Dynasty. This work was translated in Hangeul, Chosun's readers read Zhong-lie-xiao-wu-yi. This work's circulation is not clear, But this work's exciting story is interested in the readers. This work is characterized as follows: First of all, Zhong-lie-xia-yi-zhuan's charaters appear equally, the readers feels familiar. The readers like the familiar characters, because the readers read the book. The familiar characters can have a sense of speed in reading. Second, the story is continuous. Zhong-lie-xiao-wu-yi is narrated by connecting Zhong-lie-xia-yi-zhuan's story. Third, Zhong-lie-xiao-wu-yi was seeking an open ending. Classical novels prefer happy ending, this work is open ending, the expectations for the sequel became more doubled. The fourth, this work took advantage of the colloquial expressions. Zhong-lie-xiao-wu-yi is Huabenti(話本體) novel, took advantage of the spoken language. Suyu(俗語) and xiehouyu(歇後語) was represented in this work. Fifth, this work is formed a universal consensus. Ordinary people must empathize about xia-yi(俠義) and retribution, this work was well represented. Because the readers would have liked to this story.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1996.10a
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• pp.101-103
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• 1996

In this note we will discuss extension of fuzzy Lie subalgebra and fuzzy Lie ideals of a Lie algebra L on universal enveloping algebra U(L) of L and will study some relations among them.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.1123-1128
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• 1996

Let A be an (nonassociative) algebra with multiplication xy over a field F, and denote by $A^-$ the algebra with multiplication [x, y] = xy - yx$ defined on the vector space A. If $A^-$ is a Lie algebra, then A is called Lie-admissible. Lie-admissible algebras arise in various topics, including geometry of invariant affine connections on Lie groups and classical and quantum mechanics(see [2, 5, 6, 7] and references therein).

• Journal of the Korean Mathematical Society
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• v.47 no.4
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• pp.705-718
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• 2010

It gives a method to obtain a natural Lie bialgebra from a Poisson bialgebra by an algebraic point of view. Let g be a coboundary Lie bialgebra associated to a Poission Lie group G. As an application, we obtain a Lie bialgebra from a sub-Poisson bialgebra of the restricted dual of the universal enveloping algebra U(g).

• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.237-243
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• 2002

In this paper we generalize the Lie algebras of KPS's in [4], which have no toral elements. However our generalized Lie algebras have toral elements. Moreover our Lie algebras are not isomorphic to the Witt algebra W(n) with a toral element.

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.455-461
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• 2017

The Lie algebra analogue of Schur's result which is proved by Moneyhun in 1994, states that if L is a Lie algebra such that dimL/Z(L) = n, then $dimL_{(2)}={\frac{1}{2}}n(n-1)-s$ for some non-negative integer s. In the present paper, we determine the structure of central factor (for s = 0) and the factor Lie algebra $L/Z_2(L)$ (for all $s{\geq}0$) of a finite dimensional nilpotent Lie algebra L, with n-dimensional central factor. Furthermore, by using the concept of n-isoclinism, we discuss an upper bound for the dimension of $L/Z_n(L)$ in terms of $dimL_{(n+1)}$, when the factor Lie algebra $L/Z_n(L)$ is finitely generated and $n{\geq}1$.

• The KIPS Transactions:PartA
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• v.9A no.1
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• pp.99-104
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• 2002

The goal of this paper is to generalize the concept of Bezier curves and surfaces defined on the vector space $R_n$ to Lie groups, which is a new generation method of curves (called Bezier curves) on Lie groups. The defined Bezier curves and surfaces are alsways smooth because of the properties of Lie groups. We apply this method to smooth motion interpolation or smooth trajectory generation for moving rigid body in space.