Free Novikov algebras and the Hopf algebra of decorated multi-indices
Abstract
We propose a combinatorial formula for the coproduct in a Hopf algebra of decorated multi-indices 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:
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arXiv e-prints
- Pub Date:
- April 2024
- DOI:
- 10.48550/arXiv.2404.09899
- arXiv:
- arXiv:2404.09899
- Bibcode:
- 2024arXiv240409899Z
- Keywords:
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- Mathematics - Combinatorics;
- Mathematics - Rings and Algebras;
- 05C05;
- 16T30;
- 17A30
- E-Print:
- 15 pages. Erroneous Formula (16) in Version 1 removed, resulting in important changes in the proof of the main theorem