In this paper, we describe the primitive ideal space of the $C^*$-algebra $C^*(mathcal G)$  associated to the ultragraph $mathcal{G}$. We investigate the structure of the closed ideals of the quotient ultragraph $  C^* $-algebra  $C^*left(mathcal G/(H,S)right)$ which contain no nonzero set projections and then we characterize all non gauge-invariant primitive ideals. Our results generalize the ...

We describe a class of C∗-algebras which simultaneously generalise the ultragraph algebras of Tomforde and the shift space C∗-algebras of Matsumoto. In doing so we shed some new light on the different C∗-algebras that may be associated to a shift space. Finally, we show how to associate a simple C∗-algebra to an irreducible sofic shift. keywords: C∗-algebras, labelled graph, ultragraph, Matsumo...

Ultragraphs give rise to labelled graphs. We realize algebras associated such graphs as groupoid algebras, generalizing a known algebra realization of ultragraph C*-algebras any ultragraph. Then, we characterize the shift space an tight spectrum inverse semigroup with via its graph. In purely algebraic setting, show that partial action used describe Leavitt path skew group ring is equivalent du...

Given an ultragraph in the sense of Tomforde, we construct a topological quiver in the sense of Muhly and Tomforde in such a way that the universal C∗-algebras associated to the two objects coincide. We apply results of Muhly and Tomforde for topological quiver algebras and of Katsura for topological graph C∗-algebras to study the K-theory and gauge-invariant ideal structure of ultragraph C∗-al...

There are two established gradings on Leavitt path algebras associated with ultragraphs, namely the grading by integers group and free edges. In this paper, we characterize properties of these in terms underlying combinatorial ultragraphs. More precisely, when strong or epsilon-strong. The results regarding edges new also context graphs. Finally, describe relationship between strongness integer...

In this article, we give necessary and sufficient conditions under which the Leavitt path algebra $$L_K(\mathcal {G})$$ of an ultragraph $$\mathcal {G}$$ over a field K is purely infinite simple that it von Neumann regular. Consequently, obtain every graded either locally matricial algebra, or full matrix ring $$K[x, x^{-1}]$$ , algebra.

In this paper, we study representations of ultragraph Leavitt path algebras via branching systems and, using partial skew ring theory, prove the reduction theorem for these algebras. We apply to show that are semiprime and completely describe faithfulness arising from systems, in terms dynamics systems. Furthermore, permutative provide a sufficient criteria representation an algebra be equivale...

In this article, we realize the finite range ultragraph Leavitt path algebras as Steinberg algebras. This realization allows us to use groupoid approach obtain structural results about these Using skew product of groupoids, show that are graded von Neumann regular rings. We characterize strongly and every algebra is semiprimitive. Moreover, irreducible representations also can be realized Cuntz...