Leavitt path algebras of weighted Cayley graphs $C_n(S,w)$

Abstract

For a postive integer $n$ and a subset $S$ of ${\mathbb{Z}}_n$, let $⟨S⟩={\mathbb{Z}}_n$, and $w:S\to \mathbb{N}$ be a function. The weighted Cayley graph of the cyclic group ${\mathbb{Z}}_n$ with respect to $S$ and $w$ is denoted by $C_n(S,w)$. We give an explicit description of the Grothendieck group of the Leavitt path algebras of $C_n(S,w)$. We also give description of Leavitt path algebras of $C_n(S,w)$ in some special cases.

arXiv admin note: substantial text overlap with arXiv:1310.4735 and arXiv:1712.06480 by other authors