• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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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.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.9-22
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• 2014

In this paper we state some applications of Gr-category theory to the classification problem of crossed modules and to that of group extensions of the type of a crossed module.

• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.699-709
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• 2008

We study homology of the gauge group associated with the principal $G_2$ bundle over the four-sphere using the Eilenberg-Moore spectral sequence and the Serre spectral sequence with the aid of homology and cohomology operations.

• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.705-717
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• 2018

We construct some infinite series of free and nearly free curves using pencils of conics with a base locus of cardinality at most two. These curves have an interesting topology, e.g. a high degree Alexander polynomial that can be explicitly determined, a Milnor fiber homotopy equivalent to a bouquet of circles, or an irreducible translated component in the characteristic variety of their complement. Monodromy eigenspaces in the first cohomology group of the corresponding Milnor fibers are also described in terms of explicit differential forms.

• Honam Mathematical Journal
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• v.2 no.1
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• pp.19-23
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• 1980

본(本) 논문(論文)은 Cohomotopy군(群)과 Cohomolopy군(群) 사이의 몇가지 관계(關係)를 구명(究明)한 것이다. 논문(論文)의 주부분(主部分)으로서 ⅰ) 어떤 조건하(條件下)에서 $${\pi}^m(X,A){\sim_=}H^m(X,A)$$ (Theorem 2, Corollary 3) ⅱ) 어떤 조건하(條件下)에서 $${\pi}^n(X,A)=0{\Leftarrow}{\Rightarrow}H^n(X,A)=0$$ (Theorem 4) ⅲ) 어떤 조건하(條件下)에서 $${\pi}^n(X){\sim_=}{\pi}^n(A){\Leftarrow}{\Rightarrow}H^n(X){\sim_=}H^n(A)$$ (Corollary 5) 가 성립(成立)함을 증명(證明)하였다.

• Journal for History of Mathematics
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• v.20 no.4
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• pp.85-92
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• 2007

In this paper We study Some history and development of Geometry from the early 19th century to the late 20th century.

• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.183-193
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• 1995

Let N be a $II_1$ factor and G be a finite group acting outerly on N. Then the crossed product algebra $M = N \rtimes G$ is also a $II_1$ factor and $N' \cap M = CI$, i.e. N is irreducible in M. Moreover, N is regular in M, in other words, M is generated by the normalizer $N_M (N)$.

• Journal of the Korean Mathematical Society
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• v.37 no.4
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• pp.645-655
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• 2000

We calculate the R(G)-algebra structure on the reduced equivariant K-groups of two-dimensional spheres on which a compact Lie group G acts as a reflection. In particular, the reduced equivariant K-groups are trivial if G is abelian, which shows that the previous Y. Yang's calculation in [8] is incorrect.

• Journal for History of Mathematics
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• v.31 no.5
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• pp.211-222
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• 2018

This paper surveys the theory of symmetry group of differential equations. A proof of the simplest version of the Noether's theorem on conservation laws has been presented with examples in the classical mechanics. As a new approach to the conservation laws the theory of characteristic cohomology due to S. H. Wang and others has been presented.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.1
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• pp.31-35
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• 2007

In dealing with transformation group, topological approach is very natural. But, it is not sufficient to investigate geometric properties of transformation group and we need geometric method. Frankel-McDuff Conjecture is very interesting in the point that it shows struggling between topological method and geometric method. In this paper, the author suggest generalized Frankel-McDuff conjecture as a topological version of the conjecture and construct a counterexample for the generalized version, and from this we assert that topological method does not work for Frankel-McDuff Conjecture.