On a class of inverse semigroups related to Leavitt path algebras

Meakin, John; Milan, David; Wang, Zhengpan

doi:10.1016/j.aim.2021.107729

Cited by 5 publications

(7 citation statements)

References 24 publications

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“…Ash and Hall in [3] introduced these semigroups to study the nonzero J -classes of inverse semigroups. Graph inverse semigroups are closely related to the study of Leavitt path algebras [1,8] and Cuntz inverse semigroups in the C * -algebras [6,10].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Distributivity in congruence lattices of graph inverse semigroups

Luo¹,

Wang²,

Wei³

2023

Preprint

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Let Γ be a directed graph and Inv(Γ) be the graph inverse semigroup of Γ. Luo and Wang [7] showed that the congruence lattice C (Inv(Γ)) of any graph inverse semigroup Inv(Γ) is upper semimodular, but not lower semimodular in general. Anagnostopoulou-Merkouri, Mesyan and Mitchell characterized the directed graph Γ for which C (Inv(Γ)) is lower semimodular [2]. In the present paper, we show that the lower semimodularity, modularity and distributivity in the congruence lattice C (Inv(Γ)) of any graph inverse semigroup Inv(Γ) are equivalent.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Distributivity in congruence lattices of graph inverse semigroups

Luo¹,

Wang²,

Wei³

2023

Preprint

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“…Following [14], consider the multiplicative subsemigroup LI(Γ) of L F (Γ) generated by elements v ∈ V ; e, e * ∈ E ∪ E * . In [14], it is shown that LI(Γ) is an inverse semigroup, which is presented by generators v ∈ V ; e, e * ∈ E ∪ E * , and defining relations (1) − (4) plus the additional relations (5 ′ ) v = ee * , s(e) = v, where v runs over all vertices of index 1.…”

Section: Definitionsmentioning

confidence: 99%

“…•• [14] An arbitrary element of LI(Γ) can be uniquely represented as v or pq * , where p, q are paths in Γ (one of them may have zero length),…”

Section: Definitionsmentioning

confidence: 99%

“…Hall introduced graph inverse semigroups I(Γ) corresponding to an arbitrary quiver Γ. Finally, in [14], J. Meakin, D. Milan and Z. Wang introduced Leavitt inverse semigroups LI(Γ) as multiplicative subsemigroups of Leavitt path algebras L F (Γ) and, simultaneously, homeomorphic images of graph inverse semigroups I(Γ). Leavitt path algebras of polynomially bounded growth were described by A. Alahmadi, H. Alsulami, S.K.…”

Section: Introductionmentioning

confidence: 99%

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Leavitt inverse semigroups of polynomial growth

Bezushchak

2024

ADM

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“…In order to deal with actions of groups, it is interesting to work with a class of normal forms which is closed under the action of the group. This description uses only purely multiplicative expressions and is analogous to the one obtained in [43], see also [29].…”

Section: Theorem 36 (Gross-tucker For Separated Graphs) Suppose a Gro...mentioning

confidence: 99%

Free actions of groups on separated graph C*-algebras

Ara¹,

Buss²,

Costa³

2022

Preprint

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In this paper we study free actions of groups on separated graphs and their C*-algebras, generalizing previous results involving ordinary (directed) graphs.We prove a version of the Gross-Tucker theorem for separated graphs yielding a characterization of free actions on separated graphs via a skew product of the (orbit) separated graph by a group labeling function. Moreover, we describe the C*-algebras associated to these skew products as crossed products by certain coactions coming from the labeling function on the graph. Our results deal with both the full and the reduced C*-algebras of separated graphs.To prove our main results we use several techniques that involve certain canonical conditional expectations defined on the C*-algebras of separated graphs and their structure as amalgamated free products of ordinary graph C*-algebras. Moreover, we describe Fell bundles associated with the coactions of the appearing labeling functions. As a byproduct of our results, we deduce that the C*-algebras of separated graphs always have a canonical Fell bundle structure over the free group on their edges.

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On a class of inverse semigroups related to Leavitt path algebras

Cited by 5 publications

References 24 publications

Distributivity in congruence lattices of graph inverse semigroups

Distributivity in congruence lattices of graph inverse semigroups

Leavitt inverse semigroups of polynomial growth

Free actions of groups on separated graph C*-algebras

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