The van Est theorem for Rota-Baxter Lie groups

@misc{jiang2026theorem,
  title = {{The van Est theorem for Rota-Baxter Lie groups}},
  author = {Jun Jiang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.05216},
  eprint = {2610.05216},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.05216},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - The van Est theorem for Rota-Baxter Lie groups
AU  - Jun Jiang
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.05216
UR  - https://arxiv.org/abs/2610.05216
AB  - Rota-Baxter Lie groups are the group-level counterparts of Rota-Baxter Lie algebras of weight $1$. In this paper, we first establish a correspondence between representations of Rota-Baxter Lie groups and representations of Rota-Baxter Lie algebras of weight $1$ via differentiation and integration. We then develop a cohomology theory for Rota-Baxter Lie groups with coefficients in a representation by constructing an explicit cochain complex in arbitrary degrees. We justify this theory by proving a van Est type theorem, which relates the cohomology of a Rota-Baxter Lie group to that of its Rota-Baxter Lie algebra of weight $1$. As an application, we prove that equivalence classes of central extensions of a Rota-Baxter Lie group are classified by the second cohomology group.
ER  -