Graded K-theory as invariants for path algebras

这个纯数学项目的重点是莱维特路径代数，它是由有向图上的运动自然产生的结构。这些代数出现在不同的领域（如分析、非交换几何、表示理论和群论）。本项目的目的是了解莱维特路径代数的行为，并利用分级k理论对它们进行完全分类。该项目是图C*-代数（起源于澳大利亚大学的解析结构）的代数对应；这两门学科都已成为全球范围内深入研究的领域。预期的结果是分类莱维特路径代数，并找到一个桥（通过分级k理论）图C*-代数和符号动力学。

This pure mathematics project focuses on Leavitt path algebras, which are structures that naturally arise from movements on directed graphs. These algebras appear in diverse areas (eg analysis, noncommutative geometry, representation theory and group theory). The aim of this project is to understand the behaviour of Leavitt path algebras and to classify them completely by means of graded K-theory. The project is an algebraic counterpart to graph C*-algebras (analytic structures that originated in Australian universities); both subjects have become areas of intensive research globally. The expected outcomes are to classify Leavitt path algebras, and to find a bridge (via graded K-theory) to graph C*-algebras and symbolic dynamics.