• Journal of the Chungcheong Mathematical Society
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• v.19 no.2
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• pp.111-121
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• 2006

All d-homogeneous $C^*$-algebras $T^d$ over $\prod^{s_4}S^4{\times}\prod^{s_2}S^2{\times}\prod^{s_3}S^3{\times}\prod^{s_1}S^1$ are constructed. It is shown that $T^d$ are strongly Morita equivalent to $C(\prod^{s_4}S^4{\times}\prod^{s_2}S^2{\times}\prod^{s_3}S^3{\times}\prod^{s_1}S^1)$.

• The Pure and Applied Mathematics
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• v.30 no.1
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• pp.15-24
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• 2023

In this paper, we show that bounded Hochschild homology and cohomology of associated matrix Banach algebra 𝔊(𝔄, R, S, 𝔅) to a Morita context 𝔐(𝔄, R, S, 𝔅, { }, [ ]) are isomorphic to those of the Banach algebra 𝔄. Consequently, we indicate that the n-amenability and simplicial triviality of 𝔊(𝔄, R, S, 𝔅) are equivalent to the n-amenability and simplicial triviality of 𝔄.

• Bulletin of the Korean Mathematical Society
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• v.37 no.2
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• pp.249-254
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• 2000

We give an easy proof of the fact that every noncommutative torus $A_{\omega}$ is stably isomorphic to the noncommutative torus $C(\widehat{S\omega}){\;}\bigotimes{\;}A_p$ which hasa trivial bundle structure. It is well known that stable isomorphism of two separable $C^{*}-algebras$ is equibalent to the existence of eqivalence bimodule between the two stably isomorphic $C^{*}-algebras{\;}A_{\omega}$ and $C(\widehat{S\omega}){\;}\bigotimes{\;}A_p$.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.859-869
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• 1997

It is shown that for $A_{k, m}$ a k-homogeneous $C^*$-algebra over $S^{2n - 1} \times S^1$ such that no non-trivial matrix algebra can be factored out of $A_{k, m}$ and $A_{k, m} \otimes M_l(C)$ has a non-trivial bundle structure for any positive integer l, we construct an $A_{k, m^-} C(S^{2n - 1} \times S^1) \otimes M_k(C)$-equivalence bimodule to show that every k-homogeneous $C^*$-algebra over $S^{2n - 1} \times S^1)$. Moreover, we prove that the tensor product of the k-homogeneous $C^*$-algebra $A_{k, m}$ with a UHF-algebra of type $p^\infty$ has the tribial bundle structure if and only if the set of prime factors of k is a subset of the set of prime factors of pp.

• 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.