86 citations · 285 across the 46 of their papers we have counts for
54 papers
The maximal dimensions of path and graph algebras
Piotr M. Hajac, Elizabeth A. Pacheco, Łukasz Kaczmarczyk +1
We consider the class of acyclic connected directed graphs with . In this paper we find the optimal upper bound for the number of paths amongst acyclic, connected graphs w…
The functoriality of moves on graphs and the extended covariant functoriality of graph algebras
Gilles G. de Castro, Piotr M. Hajac, Mateusz Lowiel +1
Combinatorics of graphs is a very powerful tool to unravel various properties of graph algebras. In particular, isomorphisms between graph algebras are often implemented by moves b…
Milnor meets Hopf and Toeplitz at the K-theory of quantum projective planes
Francesco D'Andrea, Piotr M. Hajac, Tomasz Maszczyk +1
We explore applications of the celebrated construction of the Milnor connecting homomorphism from the odd to the even K-groups in the context of Hopf--Galois theory. For a finitely…
Relation morphisms of directed graphs
Gilles G. de Castro, Francesco D'Andrea, Piotr M. Hajac
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 ho…
Unital embeddings of Cuntz algebras from path homomorphisms of graphs
Piotr M. Hajac, Yang Liu
Cuntz algebras , , are celebrated examples of a separable infinite simple C*-algebra with a number of fascinating properties. Their K-theory allows an embedding…
The covariant functoriality of graph algebras
Piotr M. Hajac, Mariusz Tobolski
In the standard category of directed graphs, graph morphisms map edges to edges. By allowing graph morphisms to map edges to finite paths (path homomorphisms of graphs), we obtain…