Cohn-Leavitt path algebras of bi-separated graphs
| Autor: | Mohan. R, B. N. Suhas |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Discrete mathematics
Algebra and Number Theory Mathematics::Operator Algebras Mathematics::Rings and Algebras 010102 general mathematics ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION Mathematics - Rings and Algebras 010103 numerical & computational mathematics Common framework 01 natural sciences Rings and Algebras (math.RA) ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION Path (graph theory) FOS: Mathematics 0101 mathematics Mathematics |
| Zdroj: | Communications in Algebra. 49:1991-2021 |
| ISSN: | 1532-4125 0092-7872 |
| DOI: | 10.1080/00927872.2020.1861286 |
| Popis: | The purpose of this paper is to provide a common framework for studying various generalizations of Leavitt algebras and Leavitt path algebras. This paper consists of two parts. In part I we define Cohn-Leavitt path algebras of a new class of graphs with an additional structure called bi-separated graphs, which generalize the constructions of Leavitt path algebras of various types of graphs. We define and study the category \textbf{BSG} of bi-separated graphs with appropriate morphisms so that the functor which associates a bi-separated graph to its Cohn-Leavitt path algebra is continuous. We also characterize a full subcategory of \textbf{BSG} whose objects are direct limits of finite complete subobjects. We compute normal forms of these algebras and apply them to study some algebraic theoretic properties in terms of bi-separated graph-theoretic properties. In part II we specialize our attention to Cohn-Leavitt path algebras of a special class of bi-separated graphs called B-hypergraphs. We investigate their non-stable K-theory and show that the lattice of order-ideals of V-monoids of these algebras is determined by bi-separated graph-theoretic data. Using this information we study representations of Leavitt path algebras of regular hypergraphs and also find a matrix criterion for Leavitt path algebras of finite hypergraphs to have IBN property. |
| Databáze: | OpenAIRE |
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