Cohn-Leavitt path algebras of bi-separated graphs. (English) Zbl 1481.16034
An effort to combine results from \(C^*\)-algebra on Cuntz and graph operator algebras and ones of Leavitt on module types led both \(C^*\)-algebraists and ring theorists to several generalizations of path algebras by enriching ordinary directed graphs with additional structures. This long article surveys first these notions and then put them in the common frame work by a concept of bi-separated (directed) graphs. Although bi-separated graphs seem highly technical in nature, they become probably a right notion in dealing with existing generalizations of Cohn-Leavitt path algebras. Several basic, elementary properties of Cohn-Leavitt path algebras are obtained, including also a close relation between categories of bi-separated graphs and associated Cohn-Leavitt path algebras, respectively. The article could be in the interest of experts working on Leavitt path algebras.
Reviewer: Ánh Pham Ngoc (Budapest)
MSC:
| 16S88 | Leavitt path algebras |
| 16S10 | Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) |
| 16W10 | Rings with involution; Lie, Jordan and other nonassociative structures |
| 16W50 | Graded rings and modules (associative rings and algebras) |
| 16P70 | Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence (associative rings and algebras) |
| 16P90 | Growth rate, Gelfand-Kirillov dimension |
Keywords:
Cohn-Leavitt path algebras; Leavitt path algebras; Leavitt path algebras of hypergraphs; weighted Leavitt path algebrasReferences:
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