KMS weights on groupoid and graph C⁎C⁎-algebras

The paper contains a description of the KMS weights for the one-parameter action on the reduced C⁎C⁎-algebra of a second countable locally compact Hausdorff étale groupoid, arising from a continuous real valued homomorphism satisfying two conditions. The result is subsequently applied to identify the KMS weights for the gauge action on a simple graph algebra. The von Neumann algebra generated by the GNS-representation of an extremal β-KMS weight is a factor, and tools are developed to determine its type. The paper concludes with three examples to illustrate the results.