Strong Morita Equivalence for Heisenberg C*-Algebras and the Positive Cones of Their K 0-Groups
Strong Morita Equivalence for Heisenberg C*-Algebras and the Positive Cones of Their K 0-Groups
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海森堡 C* 代数及其 K 0 群的正锥的强 Morita 等价
DOI：
10.4153/cjm-1988-037-8
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发表时间：
1988
期刊：
影响因子：
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通讯作者：
J. Packer
中科院分区：
文献类型：
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作者：
J. Packer
在[14]中，我们开始研究对应于离散海森堡群的投射表示的C*-代数，并将这些C*-代数分类为 *-同构。在[14]的续篇中，我们继续研究这些所谓的Heisenberg C*-代数，首先集中研究这些C*-代数的强Morita等价类。我们在[14]中指出，如果Heisenberg C*-代数的K 0群上的正规迹的值域秩i为R的子群，则称它是i类，i <${1，2，3}; Curto，Muhly，和威廉姆斯[7]关于交叉积的强Morita等价性的研究，并与[21]和[14]的方法一起推广到沿着使我们能够构造Heisenberg C*-代数的某些强Morita等价双模。
In [14] we began a study of C*-algebras corresponding to projective representations of the discrete Heisenberg group, and classified these C*-algebras up to *-isomorphism. In this sequel to [14] we continue the study of these so-called Heisenberg C*-algebras, first concentrating our study on the strong Morita equivalence classes of these C*-algebras. We recall from [14] that a Heisenberg C*-algebra is said to be of class i, i ∊ {1, 2, 3}, if the range of any normalized trace on its K 0 group has rank i as a subgroup of R; results of Curto, Muhly, and Williams [7] on strong Morita equivalence for crossed products along with the methods of [21] and [14] enable us to construct certain strong Morita equivalence bimodules for Heisenberg C*-algebras.