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arXiv · 2610.05216

The van Est theorem for Rota-Baxter Lie groups

Jun Jiang
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Abstract

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.

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Jun Jiang. 2026-10-04. The van Est theorem for Rota-Baxter Lie groups. https://arxiv.org/abs/2610.05216

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