The graded Grothendieck group and the classification of Leavitt path algebras

Details The graded Grothendieck group and the classification of Leavitt path algebras The graded Grothendieck group and the classification of Leavitt path algebras

2011-02-20

arxiv.org/abs/1102.4088v3

Mathematics

Rings and Algebras

30 pages more polished

Scientific paper

This paper is an attempt to show that, parallel to Elliott's classification of AF $C^*$-algebras by means of $K$-theory, the graded $K_0$-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 comet and polycephaly graphs (graphs which each head is connected to a cycle or a collection of loops).

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