The Leavitt Path Algebras of Ultragraphs

DOI10.5666/KMJ.2020.60.1.21zbMath1459.16032arXiv1701.00323MaRDI QIDQ5125123

Mostafa Imanfar, Hossein Larki, Abdolrasoul Pourabbas

Publication date: 5 October 2020

Full work available at URL: https://arxiv.org/abs/1701.00323

zbMATH Keywords

Exel-Laca algebraultragraph \(C^\ast\)-algebra, Leavitt path algebra

Mathematics Subject Classification ID

Noncommutative dynamical systems (46L55) General theory of (C^*)-algebras (46L05) Leavitt path algebras (16S88)

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KMS states and continuous orbit equivalence for ultragraph shift spaces with sinks ⋮ Properties of the gradings on ultragraph algebras via the underlying combinatorics ⋮ Realizing ultragraph Leavitt path algebras as Steinberg algebras ⋮ Characterizing Rickart and Baer ultragraph Leavitt path algebras ⋮ On the ideals of ultragraph Leavitt path algebras ⋮ Leavitt path algebras of labelled graphs ⋮ On ultragraph Leavitt path algebras with finite Gelfand-Kirillov dimension ⋮ SIMPLICITY AND CHAIN CONDITIONS FOR ULTRAGRAPH LEAVITT PATH ALGEBRAS VIA PARTIAL SKEW GROUP RING THEORY ⋮ Ultragraph algebras via labelled graph groupoids, with applications to generalized uniqueness theorems ⋮ Representations and the reduction theorem for ultragraph Leavitt path algebras ⋮ Purely infinite simple ultragraph Leavitt path algebras ⋮ Irreducible and permutative representations of ultragraph Leavitt path algebras

Cites Work

• Unnamed Item
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• Cuntz-Krieger algebras of directed graphs
• A class of C*-algebras and topological Markov chains
• The \(C^*\)-algebras of row-finite graphs
• Fractional skew monoid rings.
• Uniqueness theorems and ideal structure for Leavitt path algebras
• The Leavitt path algebra of a graph.
• Kumjian-Pask algebras of higher-rank graphs
• Modules without Invariant Basis Number
• Simplicity of ultragraph algebras
• Ideal Structure of Leavitt Path Algebras with Coefficients in a Unital Commutative Ring
• Ultragraph C^*-algebras via topological quivers
• Cuntz-Krieger algebras for infinite matrices
• Primitive ideals and pure infiniteness of ultragraph $C^*$-algebras
• The 𝐶*-algebras of infinite graphs

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