Irreducible and permutative representations of ultragraph Leavitt path algebras

DOI10.1515/forum-2019-0270zbMath1441.16031arXiv1906.11602OpenAlexW2988488467MaRDI QIDQ2309638

Daniel Gonçalves, Danilo Royer

Publication date: 1 April 2020

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.11602

zbMATH Keywords

irreducible representationspermutative representationsbranching systemsultragraph Leavitt path algebras

Mathematics Subject Classification ID

Graded rings and modules (associative rings and algebras) (16W50) Representation theory of associative rings and algebras (16G99) Leavitt path algebras (16S88)

Related Items (9)

Invariant ideals in Leavitt path algebras ⋮ Realizing ultragraph Leavitt path algebras as Steinberg algebras ⋮ On the ideals of ultragraph Leavitt path algebras ⋮ Irreducibility and monicity for representations of \(k\)-graph \(C^*\)-algebras ⋮ On ultragraph Leavitt path algebras with finite Gelfand-Kirillov dimension ⋮ Representations of \(C^*\)-algebras of row-countable graphs and unitary equivalence ⋮ 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

Cites Work

• Unnamed Item
• Unitary equivalence of representations of graph algebras and branching systems
• Finitely presented simple modules over Leavitt path algebras.
• Graph \(C^\ast\)-algebras, branching systems and the Perron-Frobenius operator
• Branching systems and representations of Cohn-Leavitt path algebras of separated graphs.
• On simple modules over Leavitt path algebras.
• Irreducible representations of Leavitt path algebras.
• Ultragraphs and shift spaces over infinite alphabets
• On the representations of Leavitt path algebras.
• Realizations of AF-algebras as graph algebras, Exel-Laca algebras, and ultragraph algebras
• Separable representations, KMS states, and wavelets for higher-rank graphs
• On graded irreducible representations of Leavitt path algebras.
• Socle theory for Leavitt path algebras of arbitrary graphs.
• Continued fraction expansions and permutative representations of the Cuntz algebra \(\mathcal O_\infty\)
• Continuous shift commuting maps between ultragraph shift spaces
• The socle series of a Leavitt path algebra.
• Li-Yorke chaos for ultragraph shift spaces
• KMS and ground states on ultragraph \( C^*\)-algebras
• Representations and the reduction theorem for ultragraph Leavitt path algebras
• Ultragraph shift spaces and chaos
• On graph algebras from interval maps
• Extensions of simple modules over Leavitt path algebras.
• The socle of a Leavitt path algebra.
• Perron-Frobenius operators and representations of the Cuntz-Krieger algebras for infinite matrices
• Leavitt path algebras with at most countably many irreducible representations.
• Faithful Representations of Graph Algebras via Branching Systems
• Branching systems and general Cuntz–Krieger uniqueness theorem for ultragraph C^*-algebras
• BRANCHING SYSTEMS FOR HIGHER-RANK GRAPH C*-ALGEBRAS
• Simplicity of ultragraph algebras
• Graph algebras, Exel-Laca algebras, and ultragraph algebras coincide up to Morita equivalence
• Iterated function systems and permutation representations of the Cuntz algebra
• Primitive ideals and pure infiniteness of ultragraph $C^*$-algebras
• Monic representations of finite higher-rank graphs
• The Leavitt Path Algebras of Ultragraphs
• SIMPLICITY AND CHAIN CONDITIONS FOR ULTRAGRAPH LEAVITT PATH ALGEBRAS VIA PARTIAL SKEW GROUP RING THEORY
• Infinite Alphabet Edge Shift Spaces via Ultragraphs and Their C*-Algebras
• Wavelets and Graph C ∗-Algebras
• Leavitt Path Algebras as Partial Skew Group Rings

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