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

Chapoton, Frédéric

doi:10.2140/ant.2009.3.611

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

Frédéric Chapoton

Vol. 3 (2009), No. 6, 611–636

DOI: 10.2140/ant.2009.3.611

Abstract

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.

Keywords

tree series, operads, Lie idempotents, Bernoulli–Carlitz numbers

Mathematical Subject Classification 2000

Primary: 18D50

Secondary: 17D25, 05C05

Milestones

Received: 2 September 2008

Revised: 9 July 2009

Accepted: 16 August 2009

Published: 20 November 2009

Authors

Frédéric Chapoton
Institut Camille Jordan Université Claude Bernard Lyon 1 21 Avenue Claude Bernard 69622 Villeurbanne France
http://math.univ-lyon1.fr/~chapoton/

Vol. 3, No. 6, 2009