Rota-Baxter李群的van Est定理
The van Est theorem for Rota-Baxter Lie groups
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中文总结 AI 辅助
本文建立了Rota-Baxter李群与权为1的Rota-Baxter李代数之间的表示对应，构造了Rota-Baxter李群的上同调理论，并证明van Est定理，进而用第二上同调群分类中心扩张。
中文摘要 AI 辅助
Rota-Baxter李群是权为$1$的Rota-Baxter李代数在群层面的对应物。在本文中，我们首先通过微分与积分建立了Rota-Baxter李群的表示与权为$1$的Rota-Baxter李代数的表示之间的对应关系。随后，我们通过构造任意阶的显式上链复形，发展了系数在表示中的Rota-Baxter李群上同调理论。我们通过证明一个van Est型定理来论证该理论的合理性，该定理将Rota-Baxter李群的上同调与其权为$1$的Rota-Baxter李代数的上同调联系起来。作为应用，我们证明了Rota-Baxter李群的中心扩张的等价类由第二上同调群分类。
英文摘要
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.
发表机构
- Jilin University（吉林大学）
机构由 AI 辅助整理，请以论文原文为准。
