2025/03/30 by de Castro, Gilles G., D'Andrea, Francesco, Hajac, Piotr M. · 1 citation
#FOS: Mathematics #Operator Algebras (math.OA) #Primary: 16S88. Secondary: 46L85 #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2503.23343
Associating graph algebras to directed graphs leads to both covariant and contravariant functors from suitable categories of graphs to the category k-Alg of algebras and algebra homomorphisms. As both functors are often used at the same time, finding a new category of graphs that allows a "common denominator" functor unifying the covariant and contravariant constructions is a fundamental problem. Herein, we solve this problem by first introducing the relation category of graphs RG, and then determining the concept of admissible graph relations that yields a subcategory of RG admitting a contravariant functor to k-Alg simultaneously generalizing the aforementioned covariant and contravariant functors. Although we focus on Leavitt path algebras and graph C*-algebras, on the way we unravel functors to k-Alg given by path algebras, Cohn path algebras and Toeplitz graph C*-algebras from suitable subcategories of RG. Better still, we illustrate relation morphisms of graphs by naturally occurring examples, including Cuntz algebras, quantum spheres and quantum balls.