MORITA EQUIVALENCE FOR CROSSED PRODUCTS BY HILBERT C -BIMODULES
MORITA EQUIVALENCE FOR CROSSED PRODUCTS BY HILBERT C -BIMODULES
复制标题
HILBERT C-BIMODULES 叉积的 MORITA 等价
DOI：
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
S. Eilers
中科院分区：
文献类型：
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作者：
Beatriz Abadie;S. Eilers
本文引入了一个C-代数A与一个Hilbert C-双模X的交叉积AoXZ的概念。本文证明了：给定一个C-代数B，它带有一个循环群的半饱和作用（在这个意义上，B是由谱子空间B 0和B1生成的），则B同构于交叉积B 0 oB 1 Z.然后给出了我们的主要结果，证明了交叉积AoX Z和BoY Z是强Morita等价的，只要A和B在满足X <$A M ' M <$B Y作为A-B Hilbert C <$-双模的不变双模M下是强Morita等价的.我们还给出了Hilbert C-双模的交叉积的K-群的一个六项正合列。
We introduce the notion of the crossed product A oX Z of a C∗algebra A by a Hilbert C∗-bimodule X. It is shown that given a C∗-algebra B which carries a semi-saturated action of the circle group (in the sense that B is generated by the spectral subspaces B0 and B1), then B is isomorphic to the crossed product B0 oB1 Z. We then present our main result, in which we show that the crossed products A oX Z and B oY Z are strongly Morita equivalent to each other, provided that A and B are strongly Morita equivalent under an imprimitivity bimodule M satisfying X ⊗A M ' M ⊗B Y as A−B Hilbert C∗-bimodules. We also present a six-term exact sequence for K-groups of crossed products by Hilbert C∗-bimodules.