Free Novikov algebras and the Hopf algebra of decorated multiindices
Abstract
We propose a combinatorial formula for the coproduct in a Hopf algebra of decorated multiindices which recently appeared in the literature, which can be briefly described as the graded dual of the enveloping algebra of the free Novikov algebra generated by the set of decorations. Similarly to what happens for the Hopf algebra of rooted forests, the formula can be written in terms of admissible cuts.
 Publication:

arXiv eprints
 Pub Date:
 April 2024
 DOI:
 10.48550/arXiv.2404.09899
 arXiv:
 arXiv:2404.09899
 Bibcode:
 2024arXiv240409899Z
 Keywords:

 Mathematics  Combinatorics;
 Mathematics  Rings and Algebras;
 05C05;
 16T30;
 17A30
 EPrint:
 15 pages. Erroneous Formula (16) in Version 1 removed, resulting in important changes in the proof of the main theorem