Interesting coproducts through post-Lie algebras

Abstract: This talk reports on joint work with Annika Burmester, arxiv.org/abs/2504.19661 . We study post-Lie structures on free Lie algebras, the Grossman-Larson product on their enveloping algebras, and provide an abstract formula for its dual coproduct. This might be of interest for the general theory of post-Hopf algebras. Using a magmatic approach, we explore post-Lie algebras connected to multiple zeta values and their q-analogues. For multiple zeta values, this framework yields an algebraic interpretation of the Goncharov coproduct. Assuming that the Bernoulli numbers satisfy the so called threshold shuffle identities, we present a post-Lie structure, whose induced Lie bracket we expect to restrict to the dual of indecomposables of multiple q-zeta values.

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Audience: researchers in the topic

( paper )

Algebraic and Combinatorial Perspectives in the Mathematical Sciences

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