Hopf algebra structure of generalized quasi-symmetric functions in partially commutative variables

Adam Doliwa

Published 2016-03-10Version 1

We introduce a generalization of the Hopf algebra of quasi-symmetric functions in terms of power series in partially commutative variables. This is the graded dual of the Hopf algebra of coloured non-commutative symmetric functions described as a subalgebra of the Hopf algebra of rooted ordered coloured trees. In the Appendix we discuss the role of partial commutativity in derivation of Weyl commutation relations.