329 research outputs found
C*-algebras of separated graphs
The construction of the C*-algebra associated to a directed graph is
extended to incorporate a family consisting of partitions of the sets of
edges emanating from the vertices of . These C*-algebras are
analyzed in terms of their ideal theory and K-theory, mainly in the case of
partitions by finite sets. The groups and are
completely described via a map built from an adjacency matrix associated to
. One application determines the K-theory of the C*-algebras
, confirming a conjecture of McClanahan. A reduced
C*-algebra \Cstred(E,C) is also introduced and studied. A key tool in its
construction is the existence of canonical faithful conditional expectations
from the C*-algebra of any row-finite graph to the C*-subalgebra generated by
its vertices. Differences between \Cstred(E,C) and , such as
simplicity versus non-simplicity, are exhibited in various examples, related to
some algebras studied by McClanahan.Comment: 29 pages. Revised version, to appear in J. Functional Analysi
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