کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6414698 | 1630515 | 2014 | 30 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Kumjian-Pask algebras of locally convex higher-rank graphs Kumjian-Pask algebras of locally convex higher-rank graphs](/preview/png/6414698.png)
The Kumjian-Pask algebra of a higher-rank graph generalises the Leavitt path algebra of a directed graph. We extend the definition of Kumjian-Pask algebra to row-finite higher-rank graphs Î with sources which satisfy a local-convexity condition. After proving versions of the graded-uniqueness theorem and the Cuntz-Krieger uniqueness theorem, we study the Kumjian-Pask algebra of rank-2 Bratteli diagrams by studying certain finite subgraphs which are locally convex. We show that the desourcification procedure of Farthing and Webster yields a row-finite higher-rank graph ÎË without sources such that the Kumjian-Pask algebras of ÎË and Î are Morita equivalent. We then use the Morita equivalence to study the ideal structure of the Kumjian-Pask algebra of Î by pulling the appropriate results across the equivalence.
Journal: Journal of Algebra - Volume 399, 1 February 2014, Pages 445-474