Strongly graded groupoids and strongly graded Steinberg algebras

DOI10.1016/j.jalgebra.2019.03.030zbMath1444.16042arXiv1711.04904OpenAlexW2963437530MaRDI QIDQ2417789

Lisa Orloff Clark, Roozbeh Hazrat, Simon W. Rigby

Publication date: 29 May 2019

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

Full work available at URL: https://arxiv.org/abs/1711.04904

zbMATH Keywords

graded algebrasgroupoidsLeavitt path algebrasSteinberg algebras

Mathematics Subject Classification ID

Graded rings and modules (associative rings and algebras) (16W50) Groupoids (i.e. small categories in which all morphisms are isomorphisms) (20L05) Associative rings and algebras arising under various constructions (16S99) Leavitt path algebras (16S88)

Related Items

A note on the regular ideals of Leavitt path algebras ⋮ Strongly graded Leavitt path algebras ⋮ Properties of the gradings on ultragraph algebras via the underlying combinatorics ⋮ Strong gradings on Leavitt path algebras, Steinberg algebras and their \(C^*\)-completions ⋮ Realizing ultragraph Leavitt path algebras as Steinberg algebras ⋮ On induced graded simple modules over graded Steinberg algebras with applications to Leavitt path algebras ⋮ Graded semigroups ⋮ Equivariant dimensions of graph \(C^\ast\)-algebras ⋮ Étale Groupoids and Steinberg Algebras a Concise Introduction ⋮ Homology of étale groupoids a graded approach ⋮ Crossed product Leavitt path algebras

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The graded structure of Leavitt path algebras.
• Category equivalences involving graded modules over path algebras of quivers.
• Kumjian-Pask algebras of finitely aligned higher-rank graphs
• Graphs, groupoids, and Cuntz-Krieger algebras
• Higher-rank graph \(C^*\)-algebras: an inverse semigroup and groupoid approach
• Finite-dimensional Leavitt path algebras.
• Simplicity, primitivity and semiprimitivity of étale groupoid algebras with applications to inverse semigroup algebras
• Inverse semigroups and combinatorial \(C^*\)-algebras
• A groupoid approach to discrete inverse semigroup algebras
• Group-graded rings and modules
• A groupoid approach to C*-algebras
• The equivalence of various generalizations of group rings and modules
• Methods of graded rings.
• Graded Steinberg algebras and partial actions
• The interplay between Steinberg algebras and skew rings
• Prime étale groupoid algebras with applications to inverse semigroup and Leavitt path algebras
• Graded Steinberg algebras and their representations
• A generalized uniqueness theorem and the graded ideal structure of Steinberg algebras
• The \(C^*\)-algebras of finitely aligned higher-rank graphs
• The graded Grothendieck group and the classification of Leavitt path algebras.
• Higher rank graph \(C^*\)-algebras
• Equivalent groupoids have Morita equivalent Steinberg algebras.
• A groupoid generalisation of Leavitt path algebras
• Nonstable \(K\)-theory for graph algebras.
• The Leavitt path algebra of a graph.
• Using the Steinberg algebra model to determine the center of any Leavitt path algebra
• Growth of étale groupoids and simple algebras
• Graded Rings and Graded Grothendieck Groups
• Kumjian-Pask algebras of higher-rank graphs
• MODULES OVER ÉTALE GROUPOID ALGEBRAS AS SHEAVES
• The path space of a higher-rank graph
• The Classifying Topos of a Continuous Groupoid. I
• Reconstructing a totally disconnected groupoid from its ample semigroup
• On partial actions and groupoids
• CHAIN CONDITIONS ON ÉTALE GROUPOID ALGEBRAS WITH APPLICATIONS TO LEAVITT PATH ALGEBRAS AND INVERSE SEMIGROUP ALGEBRAS
• Diagonal-preserving graded isomorphisms of Steinberg algebras
• HIGHER-RANK GRAPHS AND THEIR $C^*$-ALGEBRAS
• On prime nonprimitive von Neumann regular algebras

This page was built for publication: Strongly graded groupoids and strongly graded Steinberg algebras