Simplicity of partial skew group rings with applications to Leavitt path algebras and topological dynamics.

DOI10.1016/j.jalgebra.2014.07.027zbMath1306.16020OpenAlexW2008107658MaRDI QIDQ743912

Danilo Royer, Johan Öinert, Daniel Gonçalves

Publication date: 1 October 2014

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2014.07.027

zbMATH Keywords

topological dynamicssimplicityLeavitt path algebrasCuntz-Krieger uniqueness theorempartial skew group ringsideal intersection property

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) General theory of (C^*)-algebras (46L05) Representations of quivers and partially ordered sets (16G20) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05) Twisted and skew group rings, crossed products (16S35)

Related Items (12)

Simplicity of algebras via epsilon-strong systems ⋮ Partial crossed products as equivalence relation algebras. ⋮ Artinian and Noetherian partial skew groupoid rings ⋮ SIMPLICITY OF LEAVITT PATH ALGEBRAS VIA GRADED RING THEORY ⋮ Polish globalization of Polish group partial actions ⋮ The interplay between Steinberg algebras and skew rings ⋮ SIMPLICITY AND CHAIN CONDITIONS FOR ULTRAGRAPH LEAVITT PATH ALGEBRAS VIA PARTIAL SKEW GROUP RING THEORY ⋮ Cohomology of partial smash products ⋮ Recent developments around partial actions ⋮ Representations of relative Cohn path algebras ⋮ SIMPLICITY OF CROSSED PRODUCTS BY TWISTED PARTIAL ACTIONS ⋮ Simplicity of skew inverse semigroup rings with applications to Steinberg algebras and topological dynamics

Cites Work

• Morita equivalence for rings without identity
• On the representations of Leavitt path algebras.
• Partial actions and partial skew group rings.
• Uniqueness theorems and ideal structure for Leavitt path algebras
• The Leavitt path algebra of a graph.
• The Ideal Intersection Property for Groupoid Graded Rings
• Simplicity of Partial Skew Group Rings of Abelian Groups
• CLOSED AND PRIME IDEALS IN PARTIAL SKEW GROUP RINGS OF ABELIAN GROUPS
• Partial dynamical systems and C*-algebras generated by partial isometries
• Associativity of crossed products by partial actions, enveloping actions and partial representations
• Simple group graded rings and maximal commutativity
• Envelope Algebras of Partial Actions as Groupoid C*-Algebras
• Simplicity of Skew Group Rings of Abelian Groups
• Leavitt Path Algebras as Partial Skew Group Rings

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