PreprintCC BY 4.0arXiv
Lie algebras for multiple Eisenstein series and multiple q-zeta values
Abstract
Racinet's double shuffle Lie algebra dm0 encodes the double shuffle relations of multiple zeta values. We study two analogues of dm0 for multiple Eisenstein series and q-analogues of multiple zeta values, namely the space BARIswap,il of swap-invariant alternil bimoulds with the uri bracket of Kühn and Schneps, and Burmester's balanced double shuffle space bm0. Both were conjectured to be Lie algebras. We prove both conjectures and show that bm0 is isomorphic to the Lie algebra of finite-depth polynomial elements of BARIswap,il.
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BibTeX
@misc{bachmann2026algebras,
title = {{Lie algebras for multiple Eisenstein series and multiple q-zeta values}},
author = {Henrik Bachmann and Hanamichi Kawamura},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29574},
eprint = {2609.29574},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29574},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Lie algebras for multiple Eisenstein series and multiple q-zeta values
AU - Henrik Bachmann
AU - Hanamichi Kawamura
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.29574
UR - https://arxiv.org/abs/2609.29574
AB - Racinet's double shuffle Lie algebra dm_0 encodes the double shuffle relations of multiple zeta values. We study two analogues of dm_0 for multiple Eisenstein series and q-analogues of multiple zeta values, namely the space BARI_swap,il of swap-invariant alternil bimoulds with the uri bracket of Kühn and Schneps, and Burmester's balanced double shuffle space bm_0. Both were conjectured to be Lie algebras. We prove both conjectures and show that bm_0 is isomorphic to the Lie algebra of finite-depth polynomial elements of BARI_swap,il.
ER -