We define and study a series indexed by rooted trees and with coefficients in . We show that it is related to a family of Lie idempotents. We prove that this series is a -deformation of a more classical series and that some of its coefficients are Carlitz -Bernoulli numbers.
"A rooted-trees $q$-series lifting a one-parameter family of Lie idempotents." Algebra Number Theory 3 (6) 611 - 636, 2009. https://doi.org/10.2140/ant.2009.3.611