Free Novikov algebras and the Hopf algebra of decorated multi-indices
arxiv（2024）
摘要
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.
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