Related papers: Labelled graphs as Morita equivalence invariants f…
We characterize the inverse semigroups that are Morita equivalent to graph inverse semigroups. We also consider a generalization to inverse semigroups associated with left cancellative categories.
We develop a technique to show the Morita equivalence of certain subrings of a ring with local units. We then apply this technique to develop conditions that are sufficient to show the Morita equivalence of subalgebras induced by partial…
A Morita equivalence similar to that found by Green for crossed products by groups will be established for crossed products by inverse semigroups. More precisely, let $G$ be an inverse semigroup, $H$ a finite sub-inverse semigroup of $G$…
We systematically develop a theory of graded semigroups, that is semigroups S partitioned by groups G, in a manner compatible with the multiplication on S. We define a smash product S#G, and show that when S has local units, the category…
In this paper we discuss graph inverse semigroups which are constucted from a directed graphs and study several interesting properties of graph inverse semigroups such as the nature of its idempotents, the structure of semilattice of…
Let $G$ be a graph and $A$ be its adjacency matrix. A graph $G$ is invertible if its adjacency matrix $A$ is invertible and the inverse of $G$ is a weighted graph with adjacency matrix $A^{-1}$. A signed graph $(G,\sigma)$ is a weighted…
In this paper we provide an abstract characterization of the inverse hulls of semigroups associated with Markov shifts. As an application of the characterization we give an example of Markov shifts that are not conjugate, but have…
We study two classes of inverse semigroups built from directed graphs, namely graph inverse semigroups and a new class of semigroups that we refer to as Leavitt inverse semigroups. These semigroups are closely related to graph…
This note extends and strengthens a theorem of Bates that says that row-finite graphs that are strong shift equivalent have Morita equivalent graph C*-algebras. This allows us to ask whether our stronger notion of Morita equivalence does in…
We study the path category of an inverse semigroup admitting unique maximal idempotents and give an abstract characterization of the inverse semigroups arising from zigzag maps on a left cancellative category. As applications we show that…
We describe how to construct all inverse semigroups Morita equivalent to a given inverse semigroup. This is done by taking the maximum inverse images of the regular Rees matrix semigroups over the inverse semigroup where the sandwich matrix…
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 investigate equivariant Morita theory for algebras with momentum maps and compute the equivariant Picard groupoid in terms of the Picard groupoid explicitly. We consider three types of Morita theory: ring-theoretic…
We classify instances of quantum pseudo-telepathy in the graph isomorphism game, exploiting the recently discovered connection between quantum information and the theory of quantum automorphism groups. Specifically, we show that graphs…
Leavitt inverse semigroups of directed finite graphs are related to Leavitt graph algebras of (directed) graphs. Leavitt path algebras of graphs have the natural $\mathbb Z$-grading via the length of paths in graphs. We consider the…
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…
It has recently been observed by Zuiddam that finite graphs form a preordered commutative semiring under the graph homomorphism preorder together with join and disjunctive product as addition and multiplication, respectively. This led to a…
The partial automorphism monoid of an inverse semigroup is an inverse monoid consisting of all isomorphisms between its inverse subsemigroups. We prove that a tightly connected fundamental inverse semigroup $S$ with no isolated nontrivial…
We prove the existence of Morita equivalences between the spin blocks at the extremal points of strings in the block-reduced crystal graph. When the parities of the core partitions are not preserved, these equivalences require crossovers,…
This is an expository paper which provides a quick introduction to Boolean inverse semigroups and their type monoids, with the emphasis on techniques and insights of the theory, and also treats the connection of the type monoid…