• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.241-246
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• 2007

For the evaluation algebra $F[e^{{\pm}x}]_M\;if\;M=\{{\partial}\}$, then $$Der_{non}(F[e^{{\pm}x}]_M)$$ of the evaluation algebra $(F[e^{{\pm}x}]_M)$ is found in the paper [15]. For $M=\{{\partial},\;{\partial}^2\}$, we find $Der_{non}(F[e^{{\pm}x}]_M))$ of the evaluation algebra $F[e^{{\pm}x}]_M$ in this paper. We show that there is a non-associative algebra which is the direct sum of derivation invariant subspaces.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.453-459
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• 2004

A left-invariant flat Riemannian connection on a Lie group makes its Lie algebra a left symmetric algebra compatible with an inner product. The left symmetric algebra is decomposed into trivial ideal and a subalgebra of e(l). Using this result, the Lie group is embedded isomorphically into the direct product of O(l) $\times$ $R^{k}$ for some nonnegative integers l and k.

• Communications of the Korean Mathematical Society
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• v.13 no.2
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• pp.225-232
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• 1998

Let H be a finite dimensional Hopf algebra over a field k, and A be an H-module algebra over k which the H-action on A is D-continuous. We show that $Q_{max}(A)$, the maximal ring or quotients of A, is an H-module algebra. This is used to prove that if H is a finite dimensional semisimple Hopf algebra and A is a semiprime right(left) Goldie algebra than $A#H$ is a semiprime right(left) Goldie algebra. Assume that Asi a semiprime H-module algebra Then $A^H$ is left Artinian if and only if A is left Artinian.

• Journal of the Korean Mathematical Society
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• v.56 no.1
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• pp.1-23
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• 2019

Let ${\mathcal{G}}$ be an ultragraph and let $C^*({\mathcal{G}})$ be the associated $C^*$-algebra introduced by Tomforde. For any gauge invariant ideal $I_{(H,B)}$ of $C^*({\mathcal{G}})$, we approach the quotient $C^*$-algebra $C^*({\mathcal{G}})/I_{(H,B)}$ by the $C^*$-algebra of finite graphs and prove versions of gauge invariant and Cuntz-Krieger uniqueness theorems for it. We then describe primitive gauge invariant ideals and determine purely infinite ultragraph $C^*$-algebras (in the sense of Kirchberg-Rørdam) via Fell bundles.

• 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.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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• pp.331-339
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• 2012

In this paper, let Q be the real quaternion algebra which consists of all quaternionic numbers, and let G be the Lie group of all automorphisms of the algebra Q. Assume that g is an arbitrary given left invariant Riemannian metric on the Lie group G. Then, we obtain a necessary and sufficient condition for an automorphism of the group G to be harmonic.

• Bulletin of the Korean Mathematical Society
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• v.40 no.4
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• pp.641-648
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• 2003

In this paper, we characterize the compact sets full-invariant properties, dual invariant properties and quasi full invariant properties in a class of infinite matrix algebras.

• Bulletin of the Korean Mathematical Society
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• v.40 no.4
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• pp.693-698
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• 2003

Various operator relationships are shown to be equivalent to the existence of an invariant subspace for an algebra of operators.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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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).

• Bulletin of the Korean Mathematical Society
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• v.30 no.2
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• pp.193-199
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• 1993

A hereditary $C^{*}$-subalgebra B of a $C^{*}$-algebra A is said to be full if B is not contained in any proper closed two-sided ideal in A, so each hereditary $C^{*}$-subalgebra of a simple $C^{*}$-algebra is always full. It is well known that every $C^{*}$-algebra is strong Morita equivalent to its full hereditary $C^{*}$-subalgebra, but the strong Morita equivalence of a $C^{*}$-algebra A and its hereditary $C^{*}$-subalgebra B does not imply the fullness of B, ingeneral. We present the following lemma for our computational convenience in the course of the proof of the main theorem. Note that $L_{B}$, $L_{B}$$^{*}$ and $L_{B}$ $L_{B}$$^{*}$ are all .alpha.-invariant whenever B is .alpha.-invariant under the action .alpha. of G.a. of G.a. of G.a. of G.f G.