Leavitt path algebras with coefficients in a commutative ring

Details Leavitt path algebras with coefficients in a commutative ring Leavitt path algebras with coefficients in a commutative ring

2009-05-04

arxiv.org/abs/0905.0478v3

Mathematics

Operator Algebras

26 pages, Version II comments: numerous typos corrected, changes made to exposition, an error in Lemma 6.1 corrected, the stat

Scientific paper

Given a directed graph E we describe a method for constructing a Leavitt path algebra $L_R(E)$ whose coefficients are in a commutative unital ring R. We prove versions of the Graded Uniqueness Theorem and Cuntz-Krieger Uniqueness Theorem for these Leavitt path algebras, giving proofs that both generalize and simplify the classical results for Leavitt path algebras over fields. We also analyze the ideal structure of $L_R(E)$, and we prove that if $K$ is a field, then $L_K(E) \cong K \otimes_\Z L_\Z(E)$.

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