\(\ast\)-isomorphism of Leavitt path algebras over \(\mathbb{Z}\)

DOI10.1016/j.aim.2017.11.018zbMath1431.16030arXiv1601.00777OpenAlexW2413732274MaRDI QIDQ1684664

Toke Meier Carlsen

Publication date: 12 December 2017

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.00777

zbMATH Keywords

Leavitt path algebrasgraph \(C^\ast\)-algebrasgraph groupoids

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Leavitt path algebras (16S88)

Related Items (10)

The complete classification of unital graph \(C^{\ast}\)-algebras: geometric and strong ⋮ Diagonal-preserving isomorphisms of étale groupoid algebras ⋮ Equivalence and stable isomorphism of groupoids, and diagonal-preserving stable isomorphisms of graph 𝐶*-algebras and Leavitt path algebras ⋮ Lifting morphisms between graded Grothendieck groups of Leavitt path algebras ⋮ Graded \(C^*\)-algebras and twisted groupoid \(C^*\)-algebras ⋮ The Groupoid Approach to Leavitt Path Algebras ⋮ Diagonal-preserving graded isomorphisms of Steinberg algebras ⋮ Flow equivalence and orbit equivalence for shifts of finite type and isomorphism of their groupoids ⋮ TENSOR PRODUCTS OF STEINBERG ALGEBRAS ⋮ A note on the centralizer of a subalgebra of the Steinberg algebra

Cites Work

• Graphs, groupoids, and Cuntz-Krieger algebras
• A topological approach to Morita equivalence for rings with local units
• Diagonal-preserving isomorphisms of étale groupoid algebras
• The commutative core of a Leavitt path algebra
• Classification of Cuntz-Krieger algebras
• Equivalent groupoids have Morita equivalent Steinberg algebras.
• Nonstable \(K\)-theory for graph algebras.
• Reconstruction of graded groupoids from graded Steinberg algebras
• Uniqueness theorems and ideal structure for Leavitt path algebras
• The Leavitt path algebra of a graph.
• Diagonal-preserving ring \(\ast\)-isomorphisms of Leavitt path algebras
• The Cuntz splice does not preserve \(\ast\)-isomorphism of Leavitt path algebras over \(\mathbb{Z}\)
• The path space of a directed graph
• Pseudo-diagonals and uniqueness theorems
• Equivalence and stable isomorphism of groupoids, and diagonal-preserving stable isomorphisms of graph 𝐶*-algebras and Leavitt path algebras
• Graph algebras and orbit equivalence
• Modules Over Rings of Words
• Modules without Invariant Basis Number
• The Module Type of a Ring
• A dynamical characterization of diagonal-preserving -isomorphisms of graph -algebras
• Isomorphism and Morita equivalence of graph algebras

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