The Socle and Semisimplicity of a Kumjian–Pask Algebra

DOI10.1080/00927872.2014.888560zbMath1330.16017arXiv1201.1888OpenAlexW1655562480MaRDI QIDQ5500704

Jonathan H. Brown, Astrid an Huef

Publication date: 7 August 2015

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.1888

zbMATH Keywords

directed graphssocleLeavitt path algebrassemisimplicityKumjian-Pask algebras

Mathematics Subject Classification ID

Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) (16S10) 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)

Related Items

Kumjian-Pask algebras of locally convex higher-rank graphs. ⋮ The cycline subalgebra of a Kumjian-Pask algebra ⋮ Unnamed Item ⋮ CHAIN CONDITIONS ON ÉTALE GROUPOID ALGEBRAS WITH APPLICATIONS TO LEAVITT PATH ALGEBRAS AND INVERSE SEMIGROUP ALGEBRAS ⋮ Centers of algebras associated to higher-rank graphs.

Cites Work

• Unnamed Item
• Graphs, groupoids, and Cuntz-Krieger algebras
• Simplicity of \(C^*\)-algebras associated to row-finite locally convex higher-rank graphs
• Purely infinite simple Leavitt path algebras.
• Finite-dimensional Leavitt path algebras.
• Algebras of quotients of path algebras.
• Socle theory for Leavitt path algebras of arbitrary graphs.
• The maximal \(C^*\)-algebra of quotients as an operator bimodule
• Separative cancellation for projective modules over exchange rings
• Extensions of exchange rings
• The socle series of a Leavitt path algebra.
• Nonstable \(K\)-theory for graph algebras.
• The socle of a Leavitt path algebra.
• Uniqueness theorems and ideal structure for Leavitt path algebras
• The Leavitt path algebra of a graph.
• Kumjian-Pask algebras of higher-rank graphs
• Gauge-Invariant Ideals in theC*-Algebras of Finitely Aligned Higher-Rank Graphs
• Periodicity in Rank 2 Graph Algebras
• HIGHER-RANK GRAPHS AND THEIR $C^*$-ALGEBRAS
• Remarks on some fundamental results about higher-rank graphs and their C*-algebras
• Chain conditions for Leavitt path algebras

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