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2014•arXiv (Cornell University)Open access

$C^*$-algebras of generalized tracial rank one

Guihua Gong, Huaxin Lin, Zhuang Niu

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Abstract

We present a classification theorem for a class of unital simple separable amenable ${\cal Z}$-stable $C^*$-algebras by the Elliott invariant. This class of simple $C^*$-algebras exhausts all possible Elliott invariant for unital stably finite simple separable amenable ${\cal Z}$-stable $C^*$-algebras. Moreover, it contains all unital simple separable amenable $C^*$-alegbras which satisfy the UCT and have finite rational tracial rank.

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What this paper is about

We present a classification theorem for a class of unital simple separable amenable ${\cal Z}$-stable $C^*$-algebras by the Elliott invariant. This class of simple $C^*$-algebras exhausts all possible Elliott invariant for unital stably finite simple separable amenable ${\cal Z}$-stable $C^*$-algebras. Moreover, it contains all unital simple separable amenable $C^*$-alegbras which satisfy the UCT and have finite rational tracial rank.

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Available abstract

We present a classification theorem for a class of unital simple separable amenable ${\cal Z}$-stable $C^*$-algebras by the Elliott invariant. This class of simple $C^*$-algebras exhausts all possible Elliott invariant for unital stably finite simple separable amenable ${\cal Z}$-stable $C^*$-algebras. Moreover, it contains all unital simple separable amenable $C^*$-alegbras which satisfy the UCT and have finite rational tracial rank.

Key concepts: Unital, Separable space, Mathematics, Simple (philosophy), Invariant (physics), Rank (graph theory), Class (philosophy), Pure mathematics

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