Embedding matrix algebras into ultragraph Leavitt path algebras and applications

Abstract

In this article, we provide criteria for an ultragraph $G$ so that for any field K and $n\ge 1$, the full matrix algebra $M_n\left(K\right)$ is embedded in the associated Leavitt path algebra of $G$. This result, which has not appeared in the context of Leavitt path algebras of graphs, is then applied to characterize properties of Lie solvable and Lie nilpotent ultragraph Leavitt path algebras, and compute the solvable index of a Lie solvable ultragraph Leavitt path algebra.