AI 中文总结
该研究刻画高阶图C*-代数的纯无限性等性质，将单UCT-Kirchberg 2-图代数的核维数1结论推广到非单高阶情形，修正了相关文献结果。
AI 中文摘要
我们研究高阶图C*-代数的结构与正则性，重点关注其核维数。对于无源头的行有限、局部凸k-图Λ，我们通过广义循环、极大尾及强非周期性刻画C*(Λ)的纯无限性，并将这些条件与本原理想空间的拓扑零维、规范不变理想的结构相关联。主要应用为：当C*(Λ)是拓扑零维的纯无限代数时，尤其当其理想格有限时，即使C*(Λ)非单，它也具有强纯无限性、𝒪_∞-稳定性且核维数为1。这将针对单UCT-Kirchberg 2-图代数的核维数1结论推广到非单的高阶情形，同时修正了现有图C*-代数文献中的若干结果。
英文摘要
We study the structure and regularity of higher rank graph $C^*$-algebras, with particular emphasis on their nuclear dimension. For a row-finite, locally convex $k$-graph $Λ$ with no sources, we characterise pure infiniteness of $C^*(Λ)$ in terms of generalised cycles, maximal tails, and strong aperiodicity, and we relate these conditions to topological dimension zero of the primitive ideal space and to the structure of gauge-invariant ideals. Our main application is that whenever $C^*(Λ)$ is purely infinite of topological dimension zero---in particular whenever its ideal lattice is finite---it is strongly purely infinite, $\mathcal O_\infty$-stable, and of nuclear dimension one, \emph{even when $C^*(Λ)$ is not simple}. This extends to the non-simple, higher-rank setting the nuclear-dimension-one computation known for simple UCT-Kirchberg $2$-graph algebras. Along the way we refine and correct several results in the existing graph $C^*$-algebra literature.
