The great challenge in writing a book about a topic of ongoing mathematical research
interest lies in determining who and what. Who are the readers for whom the book is …

The algebraic structures known as Leavitt path algebras were initially developed in 2004 by
Ara, Moreno and Pardo, and almost simultaneously (using a different approach) by the …

Let E be an arbitrary graph and K be any field. We construct various classes of non-
isomorphic simple modules over the Leavitt path algebra LK (E) induced by vertices which …

When the theory of Leavitt path algebras was already quite advanced, it was discovered that
some of the more difficult questions were susceptible to a new approach using topological …

We present a new class of graded irreducible representations of a Leavitt path algebra. This
class is new in the sense that its representation space is not isomorphic to any of the existing …

We study strongly graded groupoids, which are topological groupoids G equipped with a
continuous, surjective functor κ: G→ Γ, to a discrete group Γ, such that κ− 1 (γ) κ− 1 (δ)= κ− 1 …

Using the E-algebraic branching systems, various graded irreducible representations of a
Leavitt path K-algebra L of a directed graph E are constructed. The concept of a Laurent …

In this paper we give some sufficient and some necessary conditions for an étale groupoid
algebra to be a prime ring. As an application we recover the known primeness results for …

We say that a graded ring (-ring) is a graded quasi-Baer ring (graded quasi-Baer-ring) if, for
each graded ideal of, the right annihilator of is generated by a homogeneous idempotent …

We characterize Leavitt path algebras which are Rickart, Baer, and Baer⁎-rings in terms of
the properties of the underlying graph. In order to treat non-unital Leavitt path algebras as …