tailieunhanh - A class of corners of a Leavitt path algebra

Let E be a directed graph, K a field and LK(E) the Leavitt path algebra of E over K. The goal of this paper is to describe the structure of a class of corners of Leavitt path algebras LK(E). The motivation of this work comes from the paper “Corners of Graph Algebras” of Tyrone Crisp in which such corners of graph C*-algebras were investigated completely. | TẠP CHÍ PHÁT TRIẺN KHOA HỌC CÔNG NGHỆ CHUYÊN SAN KHOA HỌC Tự NHIÊN TẬP 2 SÔ 4 2018 75 A class of corners of a Leavitt path algebra Trinh Thanh Deo Tóm tắt Let E be a directed graph K a field and Lk E the Leavitt path algebra of E over K. The goal of this paper is to describe the structure of a class of corners of Leavitt path algebras Lk E . The motivation of this work comes from the paper Corners of Graph Algebras of Tyrone Crisp in which such corners of graph c -algebras were investigated completely. Using the same ideas of Tyrone Crisp we will show that for any finite subset X of vertices in a directed graph E such that the hereditary subset He X generated by X is finite the corner r Lk E r is isomorphic to the V X r X Leavitt path algebra Lk Ex of some graph Ex. We also provide a way how to construct this graph EX. Từ khóa Leavitt path algebra graph corner. 1 INTRODUCTION Leavitt path algebras for graphs were developed independently by two groups of mathematicians. The first group which consists of Ara Goodearl and Pardo was motivated by the K-theory of graph algebras. They introduced Leavitt path algebras 3 in order to answer analogous K-theoretic questions about the algebraic Cuntz-Krieger algebras. On the other hand Abrams and Aranda Pino introduced Leavitt path algebras Lk E in 2 to generalise Leavitt s algebras specifically the algebras Lk 1 w . The goal of this paper is to describe the structure of a class of corners of Leavitt path algebras Lk E . The motivation of this work comes from 4 in which such corners of graph c -algebras were investigated completely. Using the same ideas from 4 we will show that for any finite subset X of vertices in a directed graph E such that the hereditary subset He X generated by X is finite the corner v Lk E v is V X v X isomorphic to the Leavitt path algebra Lk Ex of some graph Ex. We also provide a way how to construct this graph EX. The graph C -algebra of an arbitrary directed graph E plays an important role in the .