• The Pure and Applied Mathematics
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• v.10 no.2
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• pp.103-118
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• 2003

We estimate the stable rank of twisted crossed products of $C^{*}-algebras$ by topological Abelian groups. As an application we estimate the stable rank of twisted crossed products of $C^{*}-algebras$ by solvable Lie groups. In particular, we obtain the stable rank estimate of twisted group $C^{*}-algebras$ of solvable Lie groups by the (reduced) dimension and (generalized) rank of groups.

• 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 $C(\widehat{S\omega}){\;}\bigotimes{\;}A_p$.

• Bulletin of the Korean Mathematical Society
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• v.43 no.1
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• pp.189-212
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• 2006

Let $F^{\alpha}G$ be a twisted group algebra with basis ${{\mu}g|g\;{\in}\;G}$ and $P\;=\;{C_g|g\;{\in}\;G}$ be a partition of G. A projective class algebra associated with P is a subalgebra of $F^{\alpha}G$ generated by all class sums $\sum\limits{_{x{\in}C_g}}\;{\mu}_x$. A main object of the paper is to find interrelationships of projective class algebras in $F^{\alpha}G$ and in $F^{\alpha}H$ for H < G. And the a-spherical function will play an important role for the purpose. We find functional properties of a-spherical functions and investigate roles of $\alpha-spherical$ functions as characters of projective class algebras.