Representations and the reduction theorem for ultragraph Leavitt path algebras

DOI10.1007/s10801-020-01004-8zbMath1470.16058arXiv1902.00013OpenAlexW3127339377MaRDI QIDQ2025127

Daniel Gonçalves, Danilo Royer

Publication date: 11 May 2021

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.00013

zbMATH Keywords

representationsreduction theoremLeavitt path algebraultragraphpartial skew-ring

Mathematics Subject Classification ID

Graded rings and modules (associative rings and algebras) (16W50) Twisted and skew group rings, crossed products (16S35) Representation theory of associative rings and algebras (16G99) Leavitt path algebras (16S88)

Related Items

Properties of the gradings on ultragraph algebras via the underlying combinatorics ⋮ Realizing ultragraph Leavitt path algebras as Steinberg algebras ⋮ On the ideals of ultragraph Leavitt path algebras ⋮ Leavitt path algebras of labelled graphs ⋮ Ultragraph algebras via labelled graph groupoids, with applications to generalized uniqueness theorems ⋮ Purely infinite simple ultragraph Leavitt path algebras ⋮ Irreducible and permutative representations of ultragraph Leavitt path algebras

Cites Work

• Unnamed Item
• Unitary equivalence of representations of graph algebras and branching systems
• Graph \(C^\ast\)-algebras, branching systems and the Perron-Frobenius operator
• Branching systems and representations of Cohn-Leavitt path algebras of separated graphs.
• Irreducible representations of Leavitt path algebras.
• Ultragraphs and shift spaces over infinite alphabets
• Cuntz-Krieger algebras and wavelets on fractals
• Leavitt path algebras with coefficients in a commutative ring.
• On the representations of Leavitt path algebras.
• Separable representations, KMS states, and wavelets for higher-rank graphs
• Leavitt path algebras with finitely presented irreducible representations.
• On graded irreducible representations of Leavitt path algebras.
• Socle theory for Leavitt path algebras of arbitrary graphs.
• A groupoid approach to discrete inverse semigroup algebras
• Graded Steinberg algebras and their representations
• Continuous shift commuting maps between ultragraph shift spaces
• Li-Yorke chaos for ultragraph shift spaces
• KMS and ground states on ultragraph \( C^*\)-algebras
• Leavitt path algebras
• Simplicity of algebras associated to étale groupoids
• Ultragraph shift spaces and chaos
• Representations of relative Cohn path algebras
• Irreducible and permutative representations of ultragraph Leavitt path algebras
• A groupoid generalisation of Leavitt path algebras
• Nonstable \(K\)-theory for graph algebras.
• The socle of a Leavitt path algebra.
• Cuntz-Krieger algebras representations from orbits of interval maps
• Perron-Frobenius operators and representations of the Cuntz-Krieger algebras for infinite matrices
• The Leavitt path algebra of a graph.
• 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
• Kumjian-Pask algebras of higher-rank graphs
• 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
• Associativity of crossed products by partial actions, enveloping actions and partial representations
• 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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