1. THE RANGES OF K-THEORETIC INVARIANTS FOR NONSIMPLE GRAPH ALGEBRAS.
- Author
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EILERS, SØREN, TAKESHI KATSURA, TOMFORDE, MARK, and WEST, JAMES
- Subjects
ALGEBRA ,K-theory ,ALGEBRAIC topology ,MATHEMATICAL sequences ,GRAPHIC methods - Abstract
There are many classes of nonsimple graph C*-algebras that are classified by the six-term exact sequence in K-theory. In this paper we consider the range of this invariant and determine which cyclic six-term exact sequences can be obtained by various classes of graph C*-algebras. To accomplish this, we establish a general method that allows us to form a graph with a given sixterm exact sequence of K-groups by splicing together smaller graphs whose C*- algebras realize portions of the six-term exact sequence. As rather immediate consequences, we obtain the first permanence results for extensions of graph C*-algebras. We are hopeful that the results and methods presented here will also prove useful in more general cases, such as situations where the C*-algebras under investigation have more than one ideal and where there are currently no relevant classification theories available. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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