Kumjian-Pask algebras of higher-rank graphs

DOI10.1090/S0002-9947-2013-05717-0zbMath1282.16006arXiv1106.4361OpenAlexW2068504889MaRDI QIDQ2846977

Gonzalo Aranda Pino, Astrid an Huef, Iain Raeburn, John Clark

Publication date: 4 September 2013

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.4361

zbMATH Keywords

Leavitt path algebrasCuntz-Krieger uniqueness theoremKumjian-Pask algebrasgraded idealsgraded-uniqueness theoremhigher rank graph \(C^*\)-algebras

Mathematics Subject Classification ID

Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) General theory of (C^*)-algebras (46L05) Representations of quivers and partially ordered sets (16G20) Graded rings and modules (associative rings and algebras) (16W50) Ideals in associative algebras (16D25)

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Prime and primitive Kumjian–Pask algebras ⋮ Construction of a class of maximal commutative subalgebras of prime Leavitt path algebras ⋮ Simplicity of algebras via epsilon-strong systems ⋮ Diagonal-preserving ring \(\ast\)-isomorphisms of Leavitt path algebras ⋮ Complex Kumjian-Pask algebras. ⋮ Kumjian-Pask algebras of locally convex higher-rank graphs. ⋮ Strongly graded groupoids and strongly graded Steinberg algebras ⋮ Purely infinite simple Kumjian-Pask algebras ⋮ Regular ideals of locally-convex higher-rank graph algebras ⋮ The interplay between Steinberg algebras and skew rings ⋮ Simple modules for Kumjian-Pask algebras ⋮ Crystal limits of compact semisimple quantum groups as higher-rank graph algebras ⋮ On induced graded simple modules over graded Steinberg algebras with applications to Leavitt path algebras ⋮ Maximal commutative subalgebras of Leavitt path algebras ⋮ Leavitt path algebras of labelled graphs ⋮ Deformations of Fell bundles and twisted graph algebras ⋮ The cycline subalgebra of a Kumjian-Pask algebra ⋮ Exel-Pardo algebras of self-similar \(k\)-graphs ⋮ Unnamed Item ⋮ \(C^\ast\)-algebras associated with Hilbert \(C^\ast\)-quad modules of finite type ⋮ Non-simple purely infinite Steinberg algebras with applications to Kumjian-Pask algebras ⋮ Leavitt path algebras over arbitrary unital rings and algebras ⋮ Ideals of Steinberg algebras of strongly effective groupoids, with applications to Leavitt path algebras ⋮ Twisted Steinberg algebras ⋮ Uniqueness theorems for Steinberg algebras ⋮ Graded Steinberg algebras and their representations ⋮ KMS weights on higher rank buildings ⋮ Cohn path algebras of higher-rank graphs ⋮ Computing the fundamental group of a higher-rank graph ⋮ Simplicity of algebras associated to étale groupoids ⋮ Representing finitely generated refinement monoids as graph monoids ⋮ Kumjian-Pask algebras of finitely aligned higher-rank graphs ⋮ Equivalent groupoids have Morita equivalent Steinberg algebras. ⋮ Centers of algebras associated to higher-rank graphs. ⋮ Representations and the reduction theorem for ultragraph Leavitt path algebras ⋮ The Leavitt Path Algebras of Ultragraphs ⋮ Dense subalgebras of purely infinite simple groupoidC*-algebras ⋮ Simplicity of skew inverse semigroup rings with applications to Steinberg algebras and topological dynamics ⋮ Simple Lie algebras arising from Steinberg algebras of Hausdorff ample groupoids ⋮ Homology of étale groupoids a graded approach ⋮ The Socle and Semisimplicity of a Kumjian–Pask Algebra ⋮ Primitivity of prime countable-dimensional regular algebras ⋮ A groupoid generalisation of Leavitt path algebras ⋮ Leavitt path algebras: the first decade ⋮ A note on the centralizer of a subalgebra of the Steinberg algebra ⋮ \(C^\ast\)-algebras associated with Hilbert \(C^\ast\)-quad modules of \(C^\ast\)-textile dynamical systems

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