• Journal of the Korean Data and Information Science Society
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• v.18 no.3
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• pp.803-808
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• 2007

In present article, we consider the embeddability problems for finite dimensional irreducible modules over a complex simple Lie algebra L. For s1(n,C) modules, we determine when one can be embedded into the other if s1(n,C) modules are tensor products of fundamental modules.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.357-365
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• 2013

Fix $n-2$ elements $h_1,{\cdots},h_{n-2}$ of the quotient field B of the polynomial algebra $\mathbb{C}[x_1,x_2,{\cdots},x_n]$. It is proved that B is a Poisson algebra with Poisson bracket defined by $\{f,g\}=det(Jac(f,g,h_1,{\cdots},h_{n-2})$ for any $f,g{\in}B$, where det(Jac) is the determinant of a Jacobian matrix.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.717-734
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• 2015

In this paper, we provide a classification of arithmetic functions in terms of identically-free-distributedness, determined by a fixed prime. We show then such classifications are free from the choice of primes. In particular, we obtain that the algebra $A_p$ of equivalence classes under the quotient on A by the identically-free-distributedness is isomorphic to an algebra $\mathbb{C}^2$, having its multiplication $({\bullet});(t_1,t_2){\bullet}(s_1,s_2)=(t_1s_1,t_1s_2+t_2s_1)$.

• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.751-763
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• 2005

For a given gauge invariant state $\omega$ on the CAR algebra A isomorphic with the C$\ast$ -algebra of $2{\times}2$ complex matrices, we construct a family of quantum Markov semigroups on A which leave w invariant. By analyzing their generators, we decompose the algebra A into four eigenspaces of the semigroups and show some properties.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.507-514
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• 2018

Let $\{{\varphi}_n\}_{n{\geq}1}$ be a sequence of analytic self-maps of ${\mathbb{D}}$. It is proved that if the union set of the ranges of the composition operators $C_{{\varphi}_n}$ on the weighted Bergman spaces contains the disk algebra, then ${\varphi}_k$ is an automorphism of ${\mathbb{D}}$ for some $k{\geq}1$.

• Kyungpook Mathematical Journal
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• v.47 no.2
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• pp.267-276
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• 2007

Injective JW-algebras are defined and are characterized by the existence of projections of norm 1 onto them. The relationship between the injectivity of a JW-algebra and the injectivity of its universal enveloping von Neumann algebra is established. The Jordan analgue of Theorem 3 of [3] is proved, that is, a JC-algebra A is nuclear if and only if its second dual $A^{**}$ is injective.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.571-579
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• 2014

In this paper, we present new vector generators of a matrix subalgebra $L_{0,n}$, which is isomorphic to the Clifford algebra $C{\ell}_{0,n}$, and we obtain the matrix form of inverse of a vector in $L_{0,n}$. Moreover, we consider the solution of a linear equation $xg_2=g_2x$, where $g_2$ is a vector generator of $L_{0,n}$.

• Kyungpook Mathematical Journal
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• v.60 no.1
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• pp.21-43
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• 2020

We introduce the Leavitt path algebras of ultragraphs and we characterize their ideal structures. We then use this notion to introduce and study the algebraic analogy of Exel-Laca algebras.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.2
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• pp.195-205
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• 2019

We consider additive mappings similar to derivations on Banach ${\ast}$-algebras and we will first study the conditions for such additive mappings on Banach ${\ast}$-algebras. Then we prove some theorems concerning approximate linear mappings of derivation-type on Banach ${\ast}$-algebras. As an application, approximate linear mappings of derivation-type on $C^{\ast}$-algebra are characterized.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.585-602
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• 2019

We characterize Gelfand-continuous functions from a Tychonoff space X into an Arens-Michael algebra A. Then we define several algebras of such functions, and investigate them as topological algebras. Finally, we provide a class of examples of (metrizable) commutative unital complete Arens-Michael algebras A and locally compact spaces X for which all these algebras differ from each other.