The classification question for Leavitt path algebras.
From MaRDI portal
Publication:950214
DOI10.1016/j.jalgebra.2008.05.020zbMath1205.16013arXiv0706.3874OpenAlexW2963891212MaRDI QIDQ950214
A. Louly, Ánh, Phạm Ngọc, Enrique Pardo Espino, Gene D. Abrams
Publication date: 22 October 2008
Published in: Journal of Algebra (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0706.3874
Grothendieck groups, (K)-theory, etc. (16E20) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) General theory of (C^*)-algebras (46L05) Representations of quivers and partially ordered sets (16G20) Leavitt path algebras (16S88)
Related Items
Leavitt path algebras are Bézout ⋮ Singular equivalence of finite dimensional algebras with radical square zero ⋮ Invariant ideals in Leavitt path algebras ⋮ Realization for tensor products of Leavitt path algebras ⋮ \(*\)-regular Leavitt path algebras of arbitrary graphs. ⋮ The graded structure of Leavitt path algebras. ⋮ Lifting graph C∗$C^*$‐algebra maps to Leavitt path algebra maps ⋮ The graded Grothendieck group and the classification of Leavitt path algebras. ⋮ Simple Lie algebras arising from Leavitt path algebras. ⋮ Grothendieck groups of purely infinite simple Leavitt path algebras for punctured power graphs of finite groups ⋮ The matrix type of purely infinite simple Leavitt path algebras. ⋮ The Dixmier-Moeglin equivalence for Leavitt path algebras. ⋮ Classifying Leavitt path algebras up to involution preserving homotopy ⋮ Weakly regular and self-injective Leavitt path algebras over arbitrary graphs. ⋮ The dynamics of Leavitt path algebras. ⋮ Connections between abelian sandpile models and the \(K\)-theory of weighted Leavitt path algebras ⋮ Comparability in the graph monoid ⋮ Flow invariants in the classification of Leavitt path algebras. ⋮ On a class of inverse semigroups related to Leavitt path algebras ⋮ Atlas of Leavitt path algebras of small graphs ⋮ Leavitt path algebras of Cayley graphs \(C_n^j\) ⋮ Leavitt Path Algebras as Partial Skew Group Rings ⋮ Regularity conditions for arbitrary Leavitt path algebras. ⋮ Isomorphism and Morita equivalence of graph algebras ⋮ Corners of Leavitt path algebras of finite graphs are Leavitt path algebras ⋮ The Leavitt path algebras of generalized Cayley graphs. ⋮ Leavitt path algebras of weighted Cayley graphs \(C_n(S,w)\) ⋮ Realizing corners of Leavitt path algebras as Steinberg algebras, with corresponding connections to graph \(C^{\ast}\)-algebras ⋮ Geometric classification of simple graph algebras ⋮ Flow equivalence of diagram categories and Leavitt path algebras ⋮ Cohn-Leavitt path algebras of bi-separated graphs ⋮ Leavitt path algebras: the first decade ⋮ On the gauge action of a Leavitt path algebra. ⋮ Leavitt \(R\)-algebras over countable graphs embed into \(L_{2,R}\).
Cites Work
- Unnamed Item
- Unnamed Item
- \(K_0\) of purely infinite simple regular rings
- Purely infinite simple Leavitt path algebras.
- A classification theorem for nuclear purely infinite simple \(C^*\)-algebras
- Nonstable \(K\)-theory for graph algebras.
- Uniqueness theorems and ideal structure for Leavitt path algebras
- The Leavitt path algebra of a graph.
- Isomorphisms between Leavitt algebras and their matrix rings
- The Module Type of a Ring
- Flow equivalence of graph algebras