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The graded Grothendieck group and the classification of Leavitt path algebras

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Abstract

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 multi-headed comets or rose graphs (graphs in which each head is connected to a cycle or to a collection of loops), or a mixture of these graphs (i.e., polycephaly graphs).

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Authors and Affiliations

  1. Department of Pure Mathematics, Queen’s University, Belfast, BT7 1NN, UK

    R. Hazrat

  2. School of Computing and Mathematics, University of Western Sydney, Penrith, NSW, 2751, Australia

    R. Hazrat

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  1. R. Hazrat
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Hazrat, R. The graded Grothendieck group and the classification of Leavitt path algebras. Math. Ann. 355, 273–325 (2013). https://doi.org/10.1007/s00208-012-0791-3

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  • DOI: https://doi.org/10.1007/s00208-012-0791-3

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