Related papers: Representing finitely generated refinement monoids…
We define a subclass of separated graphs, the class of adaptable separated graphs, and study their associated monoids. We show that these monoids are primely generated conical refinement monoids, and we explicitly determine their associated…
We show that every finitely generated conical refinement monoid can be represented as the monoid $\mathcal V(R)$ of isomorphism classes of finitely generated projective modules over a von Neumann regular ring $R$. To this end, we use the…
The Realization Problem for (von Neumann) regular rings asks what are the conical refinement monoids which can be obtained as the monoids of isomorphism classes of finitely generated projective modules over a regular ring. The analogous…
Two finitely generated monoids are constructed, one finitely presented the other not, whose (directed, unlabelled) Cayley graphs are isomorphic.
The construction of the Leavitt path algebra associated to a directed graph $E$ is extended to incorporate a family $C$ consisting of partitions of the sets of edges emanating from the vertices of $E$. The new algebras, $L_K(E,C)$, are…
Given an adaptable separated graph, we construct an associated groupoid and explore its type semigroup. Specifically, we first attach to each adaptable separated graph a corresponding semigroup, which we prove is an $E^*$-unitary inverse…
We study groupoids and semigroup C*-algebras arising from graphs of monoids, in the setting of right LCM monoids. First, we establish a general criterion when a graph of monoids gives rise to a submonoid of the fundamental group which is…
It is a conjecture that for the class of Leavitt path algebras associated to finite directed graphs, their graded Grothendieck groups $K_0^{\mathrm{gr}}$ are a complete invariant. For a Leavitt path algebra $L_{\mathsf k}(E)$, with…
A prefix monoid is a finitely generated submonoid of a finitely presented group generated by the prefixes of its defining relators. Important results of Guba (1997), and of Ivanov, Margolis and Meakin (2001), show how the word problem for…
We survey recent progress on the realization problem for von Neumann regular rings, which asks whether every countable conical refinement monoid can be realized as the monoid of isoclasses of finitely generated projective right $R$-modules…
We show that any graph product of residually finite monoids is residually finite. As a special case we obtain that any free product of residually finite monoids is residually finite. The corresponding results for graph products of…
Graph inverse semigroups generalize the polycyclic inverse monoids and play an important role in the theory of C*-algebras. This paper has two main goals: first, to provide an abstract characterization of graph inverse semigroups; and…
We compute the monoid $V(L_K(E))$ of isomorphism classes of finitely generated projective modules over certain graph algebras $L_K(E)$, and we show that this monoid satisfies the refinement property and separative cancellation. We also show…
A categorical formalism for directed graphs is introduced, featuring natural notions of morphisms and subgraphs, and leading to two elementary descriptions of the free-properad monad, first in terms of presheaves on elementary graphs,…
A partial automorphism of a finite graph is an isomorphism between its vertex induced subgraphs. The set of all partial automorphisms of a given finite graph forms an inverse monoid under composition (of partial maps). We describe the…
In this paper we define the notion of monic representation for the $C^*$-algebras of finite higher-rank graphs with no sources, and undertake a comprehensive study of them. Monic representations are the representations that, when restricted…
There is a tight relation between the geometry of a directed graph and the algebraic structure of a Leavitt path algebra associated to it. In this note, we show a similar connection between the geometry of the graph and the structure of a…
In this paper we continue the study of prime graphs of finite solvable groups. The prime graph, or Gruenberg-Kegel graph, of a finite group G has vertices consisting of the prime divisors of the order of G and an edge from primes p to q if…
In this paper, we consider certain elements in von Neumann algebras generated by graph groupoids. In particular, we are interested in finitely supported elements, called graph operators. We study the characterizations for self-adjointness,…
Let G be a finite group that acts on an abelian monoid A. If f: A -> G is a map so that f(a f(a)(b)) = f(a)f(b), for all a, b in A, then the submonoid S = {(a, f(a)) | a in A} of the associated semidirect product of A and G is said to be a…