• 한국수학교육학회지시리즈B:순수및응용수학
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• 제5권2호
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• pp.149-155
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• 1998

In this paper, we construct the minimal set of generators which generate the subgroup T of the Weyl group of Kac-Moody algebra.

• Kyungpook Mathematical Journal
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• 제48권2호
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• pp.223-232
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• 2008

We estimate the real rank of CCR C*-algebras under some assumptions. A applications we determine the real rank of the reduced group C*-algebras of non-compac connected, semi-simple and reductive Lie groups and that of the group C*-algebras of connected nilpotent Lie groups.

• 호남수학학술지
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• 제17권1호
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• pp.7-14
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• 1995

The purpose of this study is to construct the structure of the connected Lie group G with its Lie algebra $g=rad(g){\oplus}sl(2, \mathbb{F})$, which conforms to Stellmacher's [4] Pushing Up. The main idea of this paper comes from Stellmacher's [4] Pushing Up. Stelhnacher considered Pushing Up under a finite p-group. This paper, however, considers Pushing Up under the connected Lie group G with its Lie algebra $g=rad(g){\oplus}sl(2, \mathbb{F})$. In this paper, $O_p(G)$ in [4] is Q=exp(q), where q=nilrad(g) and a Sylow p-subgroup S in [7] is S=exp(s), where $s=q{\oplus}\{\(\array{0&*\\0&0}\){\mid}*{\in}\mathbb{F}\}$. Showing the properties of the connected Lie group and the subgroups of the connected Lie group with relations between a connected Lie group and its Lie algebras under the exponential map, this paper constructs the subgroup series C_z(G)

• Korean Journal of Mathematics
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• 제19권1호
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• pp.33-52
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• 2011

We prove the Hyers-Ulam stability of partitioned functional equations in Banach modules over a unital $C^*$-algebra. It is applied to show the stability of algebra homomorphisms in Banach algebras associated with partitioned functional equations in Banach algebras.

• Journal of applied mathematics & informatics
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• 제15권1_2호
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• pp.343-361
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• 2004

We prove the generalized Hyers-Ulam-Rassias stability of cyclic functional equations in Banach modules over a unital $C^{*}$-algebra. It is applied to show the stability of algebra homomorphisms between Banach algebras associated with cyclic functional equations in Banach algebras.

• 호남수학학술지
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• 제26권4호
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• pp.483-507
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• 2004

In this paper the left regular representation and the reduced $C^*$-algebra for a commutative separative semigroup is defined. The universal representation, the reduced $C^*$-algebra and the full $C^*$-algebra for the additive semigroup $N^+$ are given. Also it is proved that $C*_r(N^+){\ncong}C^*(N^+)$.

• 대한수학회지
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• 제45권2호
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• pp.575-585
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• 2008

Suppose that D is a $C^*$-discrete quantum group and $D_0$ a discrete quantum group associated with D. If there exists a continuous action of D on an operator algebra L(H) so that L(H) becomes a D-module algebra, and if the inner product on the Hilbert space H is D-invariant, there is a unique $C^*$-representation $\theta$ of D associated with the action. The fixed-point subspace under the action of D is a Von Neumann algebra, and furthermore, it is the commutant of $\theta$(D) in L(H).

• Korean Journal of Mathematics
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• 제7권1호
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• pp.71-77
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• 1999

We show that if the stable rank of $B^{\alpha}$ is one, then the stable rank of B is less than or equal to the order of G for any action of a finite group G. Also we give a short proof to the known fact that if the action of a finite group on a $C^*$-algebra B is saturated then the canonical conditional expectation from B to $B^{\alpha}$ is of index-finite type and the crossed product $C^*$-algebra is isomorphic to the algebra of compact operators on the Hilbert $B^{\alpha}$-module B.

• 대한수학회논문집
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• 제16권1호
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• pp.85-94
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• 2001

Let g=g(A) be an affine Lie algebra of type A(sub)2ι(sup)(2)(ι>1) and W be its Weyl group. In this paper, we find $\omega$$\in$W such that $\Delta$+U{1/2($\alpha$ι+$\delta$), 1/2($\alpha$ι+3$\delta$)}⊂$\Delta$+($\omega$).

• 대한수학회지
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• 제32권2호
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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 $N_M (N)$.