摘要
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,（A, B） consisting of the unitary equivalence classes of unital extensions T： A→ Q（B）. The relation between Ext,（A, B） and Ext（A, B） is established. Using this relation, we show the half-exactness of Ext,（-, B） and the （UCT） for Ext,（A, B）. Furthermore, under certain conditions, we obtain the half-exactness and Bott periodicity of Extu （A, .）.
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,（A, B） consisting of the unitary equivalence classes of unital extensions T： A→ Q（B）. The relation between Ext,（A, B） and Ext（A, B） is established. Using this relation, we show the half-exactness of Ext,（-, B） and the （UCT） for Ext,（A, B）. Furthermore, under certain conditions, we obtain the half-exactness and Bott periodicity of Extu （A, .）.
基金
Supported by National Natural Science Foundation of China （Grant No. 10771069） and Shanghai Leading Academic Discipline Project （Grant No. B407）
