The graded Grothendieck group and the classification of Leavitt path algebras
By Roozbeh Hazrat. 2011
63 citations recorded by the source corpus.
This paper is an attempt to show that, parallel to Elliott’s classification of AF C*-algebras by means of K-theory, the graded K0-group classifies Leavitt path algebras completely. In this direction, we prove this claim at two extremes, namely, for the class of acyclic graphs (graphs with no cycles) and multi-headed comets or rose graphs (graphs in which each head is connected to a cycle or to a collection of loops), or a mixture of these graphs (i.e., polycephaly graphs).
Subfields: Algebra and Number Theory, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/61675661898248ae050c6913f5c125421a1d88b0
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In Algebra and Number Theory
- Roozbeh Hazrat
- G. Abrams
- M. Tomforde
- Alexei Stepanov
- G. Pino
- Mercedes Siles Molina
- Nikolai Vavilov
- Kulumani M. Rangaswamy
In Mathematical Physics
- Roozbeh Hazrat
- G. Abrams
- M. Tomforde
- G. Pino
- Mercedes Siles Molina
- Kulumani M. Rangaswamy
- P. Ara
- Aidan Sims
In Statistical and Nonlinear Physics
Citations in the corpus
- Leavitt path algebras: the first decade (2014, background): “In fact, Hazrat in [68] makes the following Conjecture, which at first glance might seem somewhat audacious.”
- Graded Rings and Graded Grothendieck Groups (2014, methodology): “In [47] it was conjectured that the graded dimension group is a complete invariant for Leavitt path algebras.”