We introduce a special tracial Rokhlin property for unital C~*-algebras. Let A be a unital tracial rank zero C~*-algebra(or tracial rank no more than one C~*-algebra). Suppose that α : G → Aut(A) is an actio...We introduce a special tracial Rokhlin property for unital C~*-algebras. Let A be a unital tracial rank zero C~*-algebra(or tracial rank no more than one C~*-algebra). Suppose that α : G → Aut(A) is an action of a finite group G on A, which has this special tracial Rokhlin property, and suppose that A is a α-simple C~*-algebra. Then, the crossed product C~*-algebra C~*(G, A, α) has tracia rank zero(or has tracial rank no more than one). In fact,we get a more general results.展开更多
Let A be an infinite dimensional stably finite unital simple separable C^(*)-algebra.Let B■A be a stably(centrally)large subalgebra in A such that B is m-almost divisible(m-almost divisible,weakly(m,n)-divisible).The...Let A be an infinite dimensional stably finite unital simple separable C^(*)-algebra.Let B■A be a stably(centrally)large subalgebra in A such that B is m-almost divisible(m-almost divisible,weakly(m,n)-divisible).Then A is 2(m+1)-almost divisible(weakly m-almost divisible,secondly weakly(m,n)-divisible).展开更多
The authors prove that the crossed product of an infinite dimensional simple separable unital C*-algebra with stable rank one by an action of a finite group with the tracial Rokhlin property has again stable rank one....The authors prove that the crossed product of an infinite dimensional simple separable unital C*-algebra with stable rank one by an action of a finite group with the tracial Rokhlin property has again stable rank one. It is also proved that the crossed product of an infinite dimensional simple separable unital C*-algebra with real rank zero by an action of a finite group with the tracial Rokhlin property has again real rank zero.展开更多
文摘We introduce a special tracial Rokhlin property for unital C~*-algebras. Let A be a unital tracial rank zero C~*-algebra(or tracial rank no more than one C~*-algebra). Suppose that α : G → Aut(A) is an action of a finite group G on A, which has this special tracial Rokhlin property, and suppose that A is a α-simple C~*-algebra. Then, the crossed product C~*-algebra C~*(G, A, α) has tracia rank zero(or has tracial rank no more than one). In fact,we get a more general results.
基金supported by National Natural Sciences Foundation of China(11501357,11571008)supported by National Natural Sciences Foundation of China(11871375)。
文摘Let A be an infinite dimensional stably finite unital simple separable C^(*)-algebra.Let B■A be a stably(centrally)large subalgebra in A such that B is m-almost divisible(m-almost divisible,weakly(m,n)-divisible).Then A is 2(m+1)-almost divisible(weakly m-almost divisible,secondly weakly(m,n)-divisible).
基金Project supported by the National Natural Science Foundation of China (No. 10771161)
文摘The authors prove that the crossed product of an infinite dimensional simple separable unital C*-algebra with stable rank one by an action of a finite group with the tracial Rokhlin property has again stable rank one. It is also proved that the crossed product of an infinite dimensional simple separable unital C*-algebra with real rank zero by an action of a finite group with the tracial Rokhlin property has again real rank zero.