Filtered K-theory for graph algebras

Abstract

We introduce filtered algebraic $K$-theory of a ring $R$ relative to a sublattice of ideals. This is done in such a way that filtered algebraic $K$-theory of a Leavitt path algebra relative to the graded ideals is parallel to the gauge invariant filtered $K$-theory for graph $C^{\ast }$-algebras. We apply this to verify the Abrams-Tomforde conjecture for a large class of finite graphs.

16 pages

References in corpus (1)

• Geometric classification of graph $C^{\ast }$-algebras over finite graphs

Cited by in corpus (3)

• The complete classification of unital graph $C^{\ast }$-algebras: Geometric and strong
• Classification conjectures for Leavitt path algebras
• Graded $K$-Theory, Filtered $K$-theory and the classification of graph algebras