• 대한수학회논문집
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• 제10권4호
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• pp.789-795
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• 1995

For nonintegrable weight $-\rho$, some weight multiplicities of the irreducible module $L(-\rho)$ over $A^{(1)}_{(1)}$ affine Lie algebras are expressed in terms of the colored partition functions. Also we find the multiplicity of $L(-\rho)$ in ther Verma module $M(-\rho)$ for any affine Lie algebras.

• 대한수학회보
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• 제49권6호
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• pp.1199-1211
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• 2012

In this paper we give an introduction to the theory of universal central extensions of perfect Lie algebras. In particular, we will provide a model for the universal coverings of Lie tori and we show that automorphisms and derivations lift to the universal coverings. We also prove that the universal covering of a Lie ${\Lambda}$-torus of type ${\Delta}$ is again a Lie ${\Lambda}$-torus of type ${\Delta}$.

• 대한수학회지
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• 제33권4호
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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).

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제12권1호
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• pp.65-73
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• 2005

Let g = g(A) = (equation omitted) + be a symmetrizable Kac-Moody Lie algebra of type D/sub l//sup (1) with W as its Weyl group. We construct a sequence of root spaces with certain conditions. We also find the number of terms of this sequence is less then or equal to the hight of θ, the highest root.

• 대한수학회보
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• 제56권1호
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• pp.13-22
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• 2019

We compute the second cohomology of the affine Lie algebra aff(1) on the dimensional real space with coefficients in the space ${\mathcal{D}}^n_{{\underline{\lambda}},{\mu}}$ of n-ary linear differential operators acting on weighted densities where ${\underline{\lambda}}=({\lambda}_1,{\ldots},{\lambda}_n)$. We explicitly give 2-cocycles spanning these cohomology.

• 대한수학회논문집
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• 제18권3호
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• pp.439-447
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• 2003

Let (equation omitted) be a symmetrizable Kac-Moody algebra with the indecomposable generalized Cartan matrix A and W be its Weyl group. Let $\theta$ be the highest root of the corresponding finite dimensional simple Lie algebra ${\gg}$ of g. For the type ${A_N}^{(r)}$, we give an element $\omega_{o}\;\in\;W$ such that ${{\omega}_o}^{-1}({\{\Delta\Delta}_{+}})\;=\;{\{\Delta\Delta}_{-}}$. And then we prove that the degree of nilpotency of the subalgebra (equation omitted) is greater than or equal to $ht{\theta}+1$.