scholarly journals Ideal-related $K$-theory for Leavitt path algebras and graph $C^*$-algebras

2013 ◽  
Vol 62 (5) ◽  
pp. 1587-1620 ◽  
Author(s):  
Efren Ruiz ◽  
Mark Tomforde
Keyword(s):  
C Algebras ◽  
Path Algebras ◽  
K Theory ◽  
Leavitt Path Algebras

scholarly journals Cohn–Leavitt path algebras and the invariant basis number property

2019 ◽  
Vol 18 (05) ◽  
pp. 1950086 ◽  
Author(s):  
Müge Kanuni̇ ◽  
Murad Özaydin
Keyword(s):  
Finite Graph ◽  
Path Algebra ◽  
Necessary Condition ◽  
Leavitt Path Algebra ◽  
Morita Equivalent ◽  
Path Algebras ◽  
Invariant Basis ◽  
K Theory ◽  
Leavitt Path Algebras ◽  
Invariant Basis Number

We give the necessary and sufficient condition for a separated Cohn–Leavitt path algebra of a finite digraph to have Invariant Basis Number (IBN). As a consequence, separated Cohn path algebras have IBN. We determine the non-stable K-theory of a corner ring in terms of the non-stable K-theory of the ambient ring. We give a necessary condition for a corner algebra of a separated Cohn–Leavitt path algebra of a finite graph to have IBN. We provide Morita equivalent rings which are non-IBN, but are of different types.

scholarly journals Non-stable $K$-theory for Leavitt path algebras

2014 ◽  
Vol 44 (6) ◽  
pp. 1817-1850 ◽  
Author(s):  
Damon Hay ◽  
Marissa Loving ◽  
Martin Montgomery ◽  
Efren Ruiz ◽  
Katherine Todd
Keyword(s):  
Path Algebras ◽  
K Theory ◽  
Leavitt Path Algebras

scholarly journals Strongly Graded C*-algebras

2021 ◽  
Author(s):  
◽  
Ellis Dawson
Keyword(s):  
Finite Graph ◽  
C Algebra ◽  
C Algebras ◽  
Path Algebras ◽  
Leavitt Path Algebras ◽  
Necessary And Sufficient

<p>We investigate strongly graded C*-algebras. We focus on graph C*-algebras and explore the connection between graph C*-algebras and Leavitt path algebras, both of which are $\Z$-graded. It is known that a graphical condition called \emph{Condition (Y)} is necessary and sufficient for Leavitt path algebras to be strongly graded. In this thesis we prove this can be translated to the graph C*-algebra and prove that a graph C*-algebra associated to a row-finite graph is strongly graded if and only if Condition (Y) holds.</p>

scholarly journals K-theory for Leavitt path algebras: Computation and classification

2015 ◽  
Vol 433 ◽  
pp. 35-72 ◽  
Author(s):  
James Gabe ◽  
Efren Ruiz ◽  
Mark Tomforde ◽  
Tristan Whalen
Keyword(s):  
Path Algebras ◽  
K Theory ◽  
Leavitt Path Algebras

scholarly journals A class of corners of a Leavitt path algebra

2019 ◽  
Vol 2 (4) ◽  
pp. 75-81
Author(s):  
Deo Thanh Trinh
Keyword(s):  
Directed Graph ◽  
Finite Subset ◽  
Path Algebra ◽  
Graph Algebras ◽  
Leavitt Path Algebra ◽  
C Algebras ◽  
Path Algebras ◽  
Leavitt Path Algebras

Let E be a directed graph, K a field and LK(E) the Leavitt path algebra of E over K. The goal of this paper is to describe the structure of a class of corners of Leavitt path algebras LK(E). The motivation of this work comes from the paper “Corners of Graph Algebras” of Tyrone Crisp in which such corners of graph C*-algebras were investigated completely. Using the same ideas of Tyrone Crisp, we will show that for any finite subset X of vertices in a directed graph E such that the hereditary subset HE(X) generated by X is finite, the corner ( ) ( )( )     K v X v X v L E v is isomorphic to the Leavitt path algebra LK(EX) of some graph EX. We also provide a way how to construct this graph EX.

scholarly journals Strongly Graded C*-algebras

2021 ◽  
Author(s):  
◽  
Ellis Dawson
Keyword(s):  
Finite Graph ◽  
C Algebra ◽  
C Algebras ◽  
Path Algebras ◽  
Leavitt Path Algebras ◽  
Necessary And Sufficient

<p>We investigate strongly graded C*-algebras. We focus on graph C*-algebras and explore the connection between graph C*-algebras and Leavitt path algebras, both of which are $\Z$-graded. It is known that a graphical condition called \emph{Condition (Y)} is necessary and sufficient for Leavitt path algebras to be strongly graded. In this thesis we prove this can be translated to the graph C*-algebra and prove that a graph C*-algebra associated to a row-finite graph is strongly graded if and only if Condition (Y) holds.</p>

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