Cohn-Leavitt path algebras of bi-separated graphs. Issue 5 (4th May 2021)

• Record Type: Journal Article
• Authors: Mohan, R.; Suhas, B. N.
• Is Part Of: Communications in algebra. Volume 49:Issue 5(2021)
• Page Start: 1991
• Page End: 2021
• Publication Date: 2021-05-04
• Subjects: Cohn-Leavitt path algebras -- Leavitt path algebras -- Leavitt path algebras of hypergraphs -- weighted Leavitt path algebras; 16S10; 16W10; 16W50; 16P70; 16P90; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2020.1861286
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: The purpose of this article is to provide a common framework for studying various generalizations of Leavitt path algebras. We first define Cohn-Leavitt path algebras of graphs with an additional structure called bi-separated graphs. We then define and study the category BSG of bi-separated graphs with appropriate morphisms so that the functor which associates bi-separated graphs to their Cohn-Leavitt path algebras is continuous. Next, we define two sub-categories of BSG, compute basis for the algebras corresponding to one of those subcategories and study some algebraic properties in terms of bi-separated graph-theoretic properties. Finally, we compute V -monoid for some particular cases.