Leavitt path algebras: the first decade

Abstract

The algebraic structures known as {\it Leavitt path algebras} were initially developed in 2004 by Ara, Moreno and Pardo, and almost simultaneously (using a different approach) by the author and Aranda Pino. During the intervening decade, these algebras have attracted significant interest and attention, not only from ring theorists, but from analysts working in C${}^{\ast }$-algebras, group theorists, and symbolic dynamicists as well. The goal of this article is threefold: to introduce the notion of Leavitt path algebras to the general mathematical community; to present some of the important results in the subject; and to describe some of the field's currently unresolved questions.

53 pages. To appear, Bulletin of Mathematical Sciences. (page numbering in arXiv version will differ from page numbering in BMS published version; numbering of Theorems, etc ... will be the same in both versions)

References in corpus (9)

• Higher rank graph C*-algebras
• $K$-theory of Leavitt path algebras
• Structure of Leavitt path algebras of polynomial growth
• The realization problem for von Neumann regular rings
• Simple Lie algebras arising from Leavitt path algebras
• Cohn path algebras have Invariant Basis Number
• The space of Penrose tilings and the non-commutative curve with homogeneous coordinate ring k<x,y>/(y^2)
• Notes on Simple Modules over Leavitt Path Algebras
• A description of the Parry-Sullivan number of a graph using circuits