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The Leavitt path algebra of a graph

open access: yesJournal of Algebra, 2005
For any row-finite graph $E$ and any field $K$ we construct the {\its Leavitt path algebra} $L(E)$ having coefficients in $K$. When $K$ is the field of complex numbers, then $L(E)$ is the algebraic analog of the Cuntz Krieger algebra $C^*(E)$ described in [8]. The matrix rings $M_n(K)$ and the Leavitt algebras L(1,n) appear as algebras of the form $L(E)
Gonzalo Aranda Pino
exaly   +3 more sources

On the centroid of a Leavitt path algebra

open access: yesJournal of Algebraic Combinatorics
Abstract We describe the centroid of some Leavitt path algebras. More precisely, for Leavitt path algebras over a field $${{\mathbb {K}}}$$ K , we show that if the algebra is simple, then its centroid is isomorphic to
Daniel Gonçalves   +2 more
exaly   +4 more sources
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The Algebraic Entropies of the Leavitt Path Algebra and the Graph Algebra Agree

open access: yesResults in Mathematics
AbstractIn this note we prove that the algebras $$L_K(E)$$ L K ( E ) and KE have the same entropy ...
Wolfgang Böck, Candido Martin Gonzalez
exaly   +6 more sources

Ringel–Hall Algebras of Quotient Algebras of Path Algebras

Communications in Algebra, 2013
We determine the generating relations for Ringel–Hall algebras associated with quotient algebras of path algebras of Dynkin and tame quivers, and investigate their connection with composition subalgebras.
openaire   +1 more source

Counting Paths: Nondeterminism as Linear Algebra

IEEE Transactions on Software Engineering, 1984
Nondeterminism is considered to be ignorance about the actual state transition sequence performed during a computation. The number of distinct potential paths from state i to j forms a matrix \([n_{ij}]\). The behavior of a nondeterministic program is defined to be this multiplicity matrix of the state transitions.
openaire   +2 more sources

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