On Local AH algebras

Details On Local AH algebras On Local AH algebras

2011-04-04

arxiv.org/abs/1104.0445v4

Mathematics

Operator Algebras

Significant revision. It has now 91 pages

Scientific paper

We show that every unital amenable separable simple $C^*$-algebra with finite tracial rank which satisfies the UCT has in fact tracial rank at most one. We also show that unital separable simple $C^*$-algebrass which are "tracially" locally AH with slow dimension growth are ${\cal Z}$-stable. As a consequence, unital separable simple $C^*$-algebras which are locally AH with no dimension growth are isomorphic to a unital simple AH-algebra with no dimension growth.

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