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Filtered K-Theory for Graph Algebras

Part of the MATRIX Book Series book series (MXBS,volume 1)

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 algebras. We apply this to verify the Abrams-Tomforde conjecture for a large class of finite graphs.

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Acknowledgements

This work was partially supported by the Danish National Research Foundation through the Centre for Symmetry and Deformation (DNRF92), by the VILLUM FONDEN through the network for Experimental Mathematics in Number Theory, Operator Algebras, and Topology, by a grant from the Simons Foundation (# 279369 to Efren Ruiz), and by the Danish Council for Independent Research—Natural Sciences.

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Eilers, S., Restorff, G., Ruiz, E., Sørensen, A.P.W. (2018). Filtered K-Theory for Graph Algebras. In: de Gier, J., Praeger, C., Tao, T. (eds) 2016 MATRIX Annals. MATRIX Book Series, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-319-72299-3_11

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