A rooted-trees q-series lifting a one-parameter family of Lie idempotents

Frédéric Chapoton (1)

1 ICJ - Institut Camille Jordan

We define and study a series indexed by rooted trees and with coefficients in Q(q). We show that it is related to a family of Lie idempotents. We prove that this series is a q-deformation of a more classical series and that some of its coefficients are Carlitz q-Bernoulli numbers.

Mots clés: rooted tree; prelie algebra; dendriform algebra; Bernoulli number

Domaines: Algèbres quantiques [math.QA]

Frédéric Chapoton. A rooted-trees q-series lifting a one-parameter family of Lie idempotents. Algebra & Number Theory, 2009, 3 (6), pp.611-636. ⟨10.2140/ant.2009.3.611⟩. ⟨hal-00295141⟩