Filtered K-Theory for Graph Algebras
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.
Unable to display preview. Download preview PDF.
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.
- 9.Eilers, S., Restorff, G., Ruiz, E., Sørensen, A.P.W.: The complete classification of unital graph C ∗-algebras: geometric and strong. arXiv e-prints (2016, submitted)Google Scholar
- 10.Eilers, S., Restorff, G., Ruiz, E., Sørensen, A.P.W.: Geometric classification of graph C ∗-algebras over finite graphs. arXiv e-prints Canad. J. Math. (2017). https://cms.math.ca/10.4153/CJM-2017-016-7
- 14.Năstăsescu, C., van Oystaeyen, F.: Graded Ring Theory. North-Holland Mathematical Library, vol. 28. North-Holland Publishing Co., Amsterdam/New York (1982)Google Scholar
- 15.Raeburn, I.: Graph Algebras. CBMS Regional Conference Series in Mathematics, vol. 103. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI (2005)Google Scholar
- 20.Weibel, C.A.: The K-Book. Graduate Studies in Mathematics, vol. 145. American Mathematical Society, Providence, RI (2013). An introduction to algebraic K-theoryGoogle Scholar