We construct two types of unital separable simple πΆβalgebras: π΄πΆ1 π§ and π΄πΆ2 π§ , one exact but not amenable, the other nonexact. Both have the same Elliott invariant as the JiangβSu algebra β namely, π΄πΆπ π§ has a unique tracial state, πΎ0 π΄πΆπ π§ , πΎ0 π΄πΆπ π§ + , 1 π΄πΆπ π§ = (Z, Z+, 1), and πΎ1 π΄πΆπ π§ = {0} (π = 1, 2). We show that π΄πΆπ π§ (π = 1, 2) is essentially tracially in the class of separable π΅stable πΆβalgebras of nuclear dimension 1.more »
Tracial approximation in simple $C*$algebras
We revisit the notion of tracial approximation for unital simple C*algebras. We show
that a unital simple separable innite dimensional C*algebra A is asymptotically tracially
in the class of Calgebras with nite nuclear dimension if and only if A is asymptotically
tracially in the class of nuclear Zstable Calgebras.
1
 Award ID(s):
 1954600
 Publication Date:
 NSFPAR ID:
 10321035
 Journal Name:
 Canadian journal of mathematics
 ISSN:
 0008414X
 Sponsoring Org:
 National Science Foundation
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