【摘 要】
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We give a necessary and sufficient condition where a generalized inductive limit becomes a simple C*-algebra.We also show that if a unital C*-algebra can be approximately embedded into some tensorially self absorbing C*-algebra C (e.g.,uniformly hyperfini
【机 构】
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Department of Mathematics and the Research Center for Operator Algebras,East China Normal University
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We give a necessary and sufficient condition where a generalized inductive limit becomes a simple C*-algebra.We also show that if a unital C*-algebra can be approximately embedded into some tensorially self absorbing C*-algebra C (e.g.,uniformly hyperfinite (UHF)-algebras of infinite type,the Cuntz algebra O2),then we can construct a simple separable unital generalized inductive limit.When C is simple and infinite (resp.properly infinite),the construction is also infinite (resp.properly infinite).When C is simple and approximately divisible,the construction is also approximately divisible.When C is a UHF-algebra and the connecting maps satisfy a trace condition,the construction has tracial rank zero.
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