Moulds, Bimoulds, and some Lie algebras
Abstract
The Lie algebra of multiple zeta values is realized as the space ARIpolunderlineal∗ underlineil of alternal moulds whose swap is alternil up to a constant mould, equipped with the ari bracket. In this paper, we study the larger space BARIunderlineil,swappol of alternil, swap-invariant bimoulds, which is conjecturally the Lie algebra for multiple q-zeta values. We propose an explicit formula for a Lie bracket uri on this space. Moreover, we prove that the Lie algebra ARIpolunderlineal∗ underlineil embeds into BARIunderlineil,swappol, with the ari bracket translating directly into the uri bracket. Finally, we examine the associated-depth graded of BARIunderlineil,swappol, extending the known depth-graded setup for ARIunderlineal∗ underlineilpol.
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BibTeX
@misc{burmester2026moulds,
title = {{Moulds, Bimoulds, and some Lie algebras}},
author = {Annika Burmester and Ulf Kühn and Leila Schneps},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25168},
eprint = {2609.25168},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25168},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Moulds, Bimoulds, and some Lie algebras
AU - Annika Burmester
AU - Ulf Kühn
AU - Leila Schneps
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.25168
UR - https://arxiv.org/abs/2609.25168
AB - The Lie algebra of multiple zeta values is realized as the space ARI^pol_underlineal∗ underlineil of alternal moulds whose swap is alternil up to a constant mould, equipped with the ari bracket. In this paper, we study the larger space BARI_underlineil,swap^pol of alternil, swap-invariant bimoulds, which is conjecturally the Lie algebra for multiple q-zeta values. We propose an explicit formula for a Lie bracket uri on this space. Moreover, we prove that the Lie algebra ARI^pol_underlineal∗ underlineil embeds into BARI_underlineil,swap^pol, with the ari bracket translating directly into the uri bracket. Finally, we examine the associated-depth graded of BARI_underlineil,swap^pol, extending the known depth-graded setup for ARI_underlineal∗ underlineil^pol.
ER -