Graded K-Theory, Filtered K-theory and the classification of graph algebras

Abstract: We prove that an isomorphism of graded Grothendieck groups of two Leavitt path algebras induces an isomorphism of a certain quotient of algebraic filtered K-theory and consequently an isomorphism of filtered K-theory of their associated graph C*-algebras. As an application, we show that, since for a finite graph E with no sinks, the graded Grothendieck group of L(E) coincides with Krieger's dimension group of its adjacency matrix, our result relates the shift equivalence of graphs to the filtered K-theory and consequently gives that two arbitrary shift equivalent matrices give stably isomorphic graph C*-algebras. This result was only known for irreducible graphs. This is a joint work with Roozbeh Hazrat and Huanhuan Li

operator algebrasrings and algebras

Audience: researchers in the topic

Western Sydney University Abend Seminars

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