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 equivalenc...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, .）.展开更多
The goal of this paper is to investigate whether the Ext-groups of all pairs (M, N) of modules over Nakayama algebras of type (n,n,n) satisfy the condition ExtΛn(M,N)=0 for n >> 0 ? ExtΛn(M,N)=0 for n >>...The goal of this paper is to investigate whether the Ext-groups of all pairs (M, N) of modules over Nakayama algebras of type (n,n,n) satisfy the condition ExtΛn(M,N)=0 for n >> 0 ? ExtΛn(M,N)=0 for n >> 0. We achieve that by discussing the Ext-groups of Nakayama algebra with projectives of lengths 3n+1 and 3n+2 using combinations of modules of different lengths.展开更多
This paper concerns classifying completely positive maps between certain C*-algebras. Several invariants for classifying completely positive maps are constructed. It is proved that one of them is isomorphic to the Ext...This paper concerns classifying completely positive maps between certain C*-algebras. Several invariants for classifying completely positive maps are constructed. It is proved that one of them is isomorphic to the Ext-group of C*-algebra extensions in special circumstances. Furthermore, this invariant induces a functor from C*-algebras to abelian groups which is split-exact.展开更多
基金Supported by National Natural Science Foundation of China （Grant No. 10771069） and Shanghai Leading Academic Discipline Project （Grant No. B407）
文摘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, .）.
文摘The goal of this paper is to investigate whether the Ext-groups of all pairs (M, N) of modules over Nakayama algebras of type (n,n,n) satisfy the condition ExtΛn(M,N)=0 for n >> 0 ? ExtΛn(M,N)=0 for n >> 0. We achieve that by discussing the Ext-groups of Nakayama algebra with projectives of lengths 3n+1 and 3n+2 using combinations of modules of different lengths.
文摘This paper concerns classifying completely positive maps between certain C*-algebras. Several invariants for classifying completely positive maps are constructed. It is proved that one of them is isomorphic to the Ext-group of C*-algebra extensions in special circumstances. Furthermore, this invariant induces a functor from C*-algebras to abelian groups which is split-exact.
