Ideal-related $K$-theory for Leavitt path algebras and graph $C^*$-algebras
نویسندگان
چکیده
منابع مشابه
Algebras of Quotients of Leavitt Path Algebras
We start this paper by showing that the Leavitt path algebra of a (row-finite) graph is an algebra of quotients of the corresponding path algebra. The path algebra is semiprime if and only if whenever there is a path connecting two vertices, there is another one in the opposite direction. Semiprimeness is studied because, for acyclic graphs, the Leavitt path algebra is a Fountain-Gould algebra ...
متن کاملWeakly Noetherian Leavitt Path Algebras
We study row-finite Leavitt path algebras. We characterize the row-finite graphs E for which the Leavitt path algebra is weakly Noetherian. Our main result is that a Leavitt path algebra is weakly Noetherian if and only if there is ascending chain condition on the hereditary and saturated closures of the subsets of the vertices of the graph E.
متن کاملChain Conditions for Leavitt Path Algebras
In this paper, results known about the artinian and noetherian conditions for the Leavitt path algebras of graphs with finitely many vertices are extended to all row-finite graphs. In our first main result, necessary and sufficient conditions on a row-finite graph E are given so that the corresponding (not necessarily unital) Leavitt path K-algebra L(E) is semisimple. These are precisely the al...
متن کاملSocle Theory for Leavitt Path Algebras of Arbitrary Graphs
The main aim of the paper is to give a socle theory for Leavitt path algebras of arbitrary graphs. We use both the desingularization process and combinatorial methods to study Morita invariant properties concerning the socle and to characterize it, respectively. Leavitt path algebras with nonzero socle are described as those which have line points, and it is shown that the line points generate ...
متن کاملRegularity conditions for arbitrary Leavitt path algebras
We show that if E is an arbitrary acyclic graph then the Leavitt path algebra LK(E) is locally K-matricial; that is, LK(E) is the direct union of subalgebras, each isomorphic to a finite direct sum of finite matrix rings over the fieldK. As a consequence we get our main result, in which we show that the following conditions are equivalent for an arbitrary graph E: (1) LK (E) is von Neumann regu...
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ژورنال
عنوان ژورنال: Indiana University Mathematics Journal
سال: 2013
ISSN: 0022-2518
DOI: 10.1512/iumj.2013.62.5123