Purely infinite simple ultragraph Leavitt path algebras

2020/07/16 by Nam, Tran Giang, Nam, Nguyen Dinh
#05C25 #16S88 #16S99 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2007.08144

Abstract

In this article, we give necessary and sufficient conditions under which the Leavitt path algebra L_K(G) of an ultragraph G over a field K is purely infinite simple and that it is von Neumann regular. Consequently, we obtain that every graded simple ultragraph Leavitt path algebra is either a locally matricial algebra, or a full matrix ring over K[x, x^-1], or a purely infinite simple algebra.

Related

• Realizing ultragraph Leavitt path algebras as Steinberg algebras
• Characterizing Rickart and Baer ultragraph Leavitt path algebras
• Morita Equivalence of Graph and Ultragraph Leavitt Path Algebras
• Purely infinite simple Leavitt path algebras
• On the ideals of ultragraph Leavitt path algebras