• 대한수학회보
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• 제60권2호
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• pp.529-539
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• 2023

In this paper, we study nuclearity of semigroup crossed products for quasi-lattice ordered groups. We show the relationships among nuclearity of the semigroup crossed product, amenability of the quasi-lattice ordered group and nuclearity of the underlying C^*-algebra.

• 대한수학회지
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• 제36권1호
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• pp.97-107
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• 1999

Given a C-dynamical system (A, G, $\alpha$) with a locally compact group G, two kinds of C-algebras are made from it, called the full C-crossed product and the reduced C-crossed product. In this paper, we extend the theory of the classical C-crossed product to the C-dynamical system (A, G, $\alpha$) with a left-cancellative semigroup M with unit. We construct a new C-algebra A $\alpha$rM, the reduced crossed product of A by the semigroup M under the action $\alpha$ and investigate some properties of A $\alpha$rM.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제14권4호
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• pp.307-315
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• 2007

We study crossed products of the free group and semigroup $C^*-algebras$ by actions of ${\mathbb{R}$, i.e., flows, and estimate and compute their stable rank.

• 대한수학회지
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• 제52권4호
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• pp.869-889
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• 2015

Let ${\Gamma}^+$ be the positive cone in a totally ordered abelian group ${\Gamma}$, and ${\alpha}$ an action of ${\Gamma}^+$ by extendible endomorphisms of a $C^*$-algebra A. Suppose I is an extendible ${\alpha}$-invariant ideal of A. We prove that the partial-isometric crossed product $\mathcal{I}:=I{\times}^{piso}_{\alpha}{\Gamma}^+$ embeds naturally as an ideal of $A{\times}^{piso}_{\alpha}{\Gamma}^+$, such that the quotient is the partial-isometric crossed product of the quotient algebra. We claim that this ideal $\mathcal{I}$ together with the kernel of a natural homomorphism $\phi:A{\times}^{piso}_{\alpha}{\Gamma}^+{\rightarrow}A{\times}^{iso}_{\alpha}{\Gamma}^+$ gives a composition series of ideals of $A{\times}^{piso}_{\alpha}{\Gamma}^+$ studied by Lindiarni and Raeburn.

• East Asian mathematical journal
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• 제21권2호
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• pp.151-161
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• 2005

We analyze the structure of $C^*-algebras$ generated by left regular isometric representations of semigroups.