arXiv subjects

N. T. Phuc

Publications and source records attributed to N. T. Phuc.

3 recordsLinked to original sources

arXiv2023

On Leavitt path algebras of Hopf graphs

In this paper, we provide the structure of Hopf graphs associated to pairs $(G, \mathfrak{r})$ consisting of groups $G$ together with ramification datas $\mathfrak{r}$ and their Leavitt path algebras. Consequently, we characterize the Gelfand-Kirillov dimension, the stable rank, the purely infinite simplicity and the existence of a nonzero finite dimensional representation of the Leavitt path algebra of a Hopf graph via properties of ramification data $\mathfrak{r}$ and $G$.

math.RA↗

arXiv2016

A criterion for Leavitt path algebras having invariant basis number

In this paper, we give a matrix-theoretic criterion for the Leavitt path algebra of a finite graph has Invariant Basis Number. Consequently, we show that the Cohn path algebra of a finite graph has Invariant Basis Number, as well as provide some certain classes of finite graphs for which Leavitt path algebras having Invariant Basis Number.

math.RA↗

arXiv2016

Leavitt path algebras having Unbounded Generating Number

We present a result of P. Ara which establishes that the Unbounded Generating Number property is a Morita invariant for unital rings. Using this, we give necessary and sufficient conditions on a graph $E$ so that the Leavitt path algebra associated to $E$ has UGN. We conclude by identifying the graphs for which the Leavitt path algebra is (equivalently) directly finite; stably finite; Hermite; and has cancellation of projectives.

math.RA↗