Irreducible and permutative representations of ultragraph Leavitt path algebras
نویسندگان
چکیده
منابع مشابه
Weakly 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 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 کاملGeneralized permutative representations of the Cuntz algebras
We introduce representations of the Cuntz algebra ON which are parameterized by sequences in the set of unit vectors inC . These representations are natural generalization of permutative representations by Bratteli-Jorgensen and Davidson-Pitts. We show their existence, irreducibility, equivalence, uniqueness of irreducible decomposition and decomposition formulae by using parameters of represen...
متن کاملThe 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 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: Forum Mathematicum
سال: 2020
ISSN: 0933-7741,1435-5337
DOI: 10.1515/forum-2019-0270