• 대한수학회논문집
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• 제37권4호
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• pp.1181-1197
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• 2022

We give a complete classification of simply connected and solvable real Lie groups whose nontrivial coadjoint orbits are of codimension 1. This classification of the Lie groups is one to one corresponding to the classification of their Lie algebras. Such a Lie group belongs to a class, called the class of MD-groups. The Lie algebra of an MD-group is called an MD-algebra. Some interest properties of MD-algebras will be investigated as well.

• 대한수학회지
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• 제33권2호
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• pp.387-397
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• 1996

Let G be a finite group and F be a field of characteristic $p \geq 0$. Let $\Gamma = F^f G$ be a twisted group algebra corresponding to a 2-cocycle $f \in Z^2(G,F^*), where F^* = F - {0}$ is the multiplicative subgroup of F.

• 대한수학회보
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• 제33권4호
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• pp.531-536
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• 1996

Let $F$ denote $R$ or $C$. Put $A = SL(2, F)$. Define $P(F^2)$ to be the set of all 1-dimensional subspaces of $F^2$. Then the natural action of A on $F^2$ induces an action on $P(F^2)$.

• 한국수학사학회지
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• 제22권1호
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• pp.89-110
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• 2009

본 논문은 수학수업에서 점점 소외되고 있는 수학학습부진아가 대수학습에서 학업성취도를 신장시키기 위해 좀 더 나은 효과를 얻을 수 있는 방법을 모색하고자 하였다. 이를 위해 수학학습부진아를 선정하여 두 집단으로 나누었다. 한 집단은 처치집단으로 CAS 계산기를 사용하여 활동지를 학습하고, 다른 집단은 통제집단으로 지필을 사용하여 활동지를 학습하였다. 각 집단은 활동지를 통해서 메타인지 활동을 하였다. 수업 전과 후에 두 집단 모두 지필로 수학학업성취도를 실시하여 비교 분석한 결과, 처치집단이 통제집단보다 여러 가지 측면에서 더 나은 효과를 나타내는 것을 확인하였다.

• 대한수학회보
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• 제48권3호
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• pp.469-474
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• 2011

The Kauffman bracket skein module $K_t$(M) of a 3-manifold M becomes an algebra for t = -1. We prove that this algebra has no non-trivial nilpotent elements for M being the exterior of the twist knot in 3-sphere and, therefore, it is isomorphic to the $SL_2(\mathbb{C})$-character ring of the fundamental group of M. Our proof is based on some properties of Chebyshev polynomials.

• 대한수학회보
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• 제53권6호
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• pp.1685-1695
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• 2016

In this article we consider Lie super-bialgebra structures on the generalized loop super-Virasoro algebra ${\mathcal{G}}$. By proving that the first cohomology group $H^1({\mathcal{G}},{\mathcal{G}}{\otimes}{\mathcal{G}})$ is trivial, we obtain that all such Lie bialgebras are triangular coboundary.

• 대한수학회논문집
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• 제10권3호
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• pp.653-659
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• 1995

We prove that two essentially normal elements of a type $II_{\infty}$ factor von Neumann algebra are unitarily equivalent up to the compact ideal if and only if they have the identical essential spectrum and the same index data. Also we calculate the spectrum and essential spectrum of a non-unitary isometry of von Neumann algebra.

• 대한수학회지
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• 제53권3호
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• pp.489-501
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• 2016

In this paper, we study the rigidity under $K{\ddot{a}}hler$ deformation of the complex structure of odd Lagrangian Grassmannians, i.e., the Lagrangian case $Gr_{\omega}$(n, 2n+1) of odd symplectic Grassmannians. To obtain the global deformation rigidity of the odd Lagrangian Grassmannian, we use results about the automorphism group of this manifold, the Lie algebra of infinitesimal automorphisms of the affine cone of the variety of minimal rational tangents and its prolongations.

• 호남수학학술지
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• 제29권2호
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• pp.269-277
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• 2007

Let L := L(G) denote the classical modular Lie algebra of $E_6$-type over an algebraically closed field F of characteristic p > 5 associated with some simple and simply connected algebraic group G. After the prototypes of those for $E_8$-type in [4], we shall search for irreducible (=simple) L-modules in this paper.

• 대한수학회논문집
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• 제17권3호
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• pp.475-485
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• 2002

We estimate the stable rank, connected stable rank and general stable rank of the multiplier algebras of $C^{＊}$-algebras under some conditions and prove that the ranks of them are infinite. Moreover, we show that for any $\sigma$-unital subhomogeneous $C^{＊}$-algebra, its stable rank is equal to that of its multiplier algebra.