PreprintCC BY 4.0arXiv
An sl2-action on the uri Lie algebra
Abstract
We construct an sl2-action by derivations on the Lie algebra B of swap invariant alternil bimoulds with the uri bracket of Kühn and Schneps. This Lie algebra plays the role for formal multiple Eisenstein series which Racinet's double shuffle Lie algebra dm0 plays for multiple zeta values. The kernel m of the lowering operator is a Lie subalgebra, B is the direct sum of its iterates under the raising operator, and this gives Rankin-Cohen type operators on m. We define a Lie subalgebra d of B and show that it is isomorphic to dm0 extended by an additional element in weight one.
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BibTeX
@misc{bachmann2026sl2action,
title = {{An $\mathfraksl_2$-action on the uri Lie algebra}},
author = {Henrik Bachmann},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02137},
eprint = {2609.02137},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02137},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An sl_2-action on the uri Lie algebra
AU - Henrik Bachmann
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.02137
UR - https://arxiv.org/abs/2609.02137
AB - We construct an sl_2-action by derivations on the Lie algebra B of swap invariant alternil bimoulds with the uri bracket of Kühn and Schneps. This Lie algebra plays the role for formal multiple Eisenstein series which Racinet's double shuffle Lie algebra dm_0 plays for multiple zeta values. The kernel m of the lowering operator is a Lie subalgebra, B is the direct sum of its iterates under the raising operator, and this gives Rankin-Cohen type operators on m. We define a Lie subalgebra d of B and show that it is isomorphic to dm_0 extended by an additional element in weight one.
ER -