LEAVITT PATH ALGEBRAS OF WEIGHTED AND SEPARATED GRAPHS
نویسندگان
چکیده
Abstract In this paper, we show that Leavitt path algebras of weighted graphs and separated are intimately related. We prove any algebra $L(E,\omega )$ a row-finite vertex graph $(E,\omega is $*$ -isomorphic to the lower certain bipartite $(E(\omega ),C(\omega ))$ . For general locally finite $(E, \omega , quotient $L_1(E,\omega an upper another $(E(w)_1,C(w)^1)$ furthermore introduce ${L^{\mathrm {ab}}} (E,w)$ which universal tame -algebra generated by set partial isometries. draw some consequences our results for structure ideals study in detail two different maximal $L(m,n)$
منابع مشابه
The Leavitt path algebras of arbitrary graphs
We extend the notion of the Leavitt path algebra of a graph E to include all directed graphs. We show how various ring-theoretic properties of these more general structures relate to the corresponding properties of Leavitt path algebras of row-finite graphs. Specifically, we identify those graphs for which the corresponding Leavitt path algebra is simple; purely infinite simple; exchange; and s...
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 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 کاملAlgebras 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 کاملLeavitt Path Algebras and Direct Limits
An introduction to Leavitt path algebras of arbitrary directed graphs is presented, and direct limit techniques are developed, with which many results that had previously been proved for countable graphs can be extended to uncountable ones. Such results include characterizations of simplicity, characterizations of the exchange property, and cancellation conditions for the K-theoretic monoid of ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of The Australian Mathematical Society
سال: 2022
ISSN: ['1446-8107', '1446-7887']
DOI: https://doi.org/10.1017/s1446788722000155