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arXiv · 1008.1295

The Ext--Group of Unitary Equivalence Classes of Unital Extensions

Yifeng Xue
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Abstract

Let $\A$ be a unital separable nuclear $C^*$--algebra which belongs to the bootstrap category $\N$ and $\B$ be a separable stable $C^*$--algebra. In this paper, we consider the group $\Ext_u(\A,\B)$ consisting of the unitary equivalence classes of unital extensions $\tau\colon\A\rightarrow Q(\B)$. The relation between $\Ext_u(\A,\B)$ and $\Ext(\A,\B)$ is established. Using this relation, we show the half--exactness of $\Ext_u(\cdot,\B)$ and the (UCT) for $\Ext_u(\A,\B)$. Furthermore, under certain conditions, we obtain the half--exactness and Bott periodicity of $\Ext_u(\A,\cdot)$.

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Yifeng Xue. 2010-08-07. The Ext--Group of Unitary Equivalence Classes of Unital Extensions. https://arxiv.org/abs/1008.1295

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