秩一乘积格的非交换拓扑因子定理
The noncommutative topological factor theorem for rank-one product lattices
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中文总结 AI 辅助
本文证明实秩一单李群乘积中不可约格的非交换拓扑因子定理，其结论可推广至树及混合局部域版本，且$\text{SL}_3(\boldsymbol{Z})$全旗作用的对应分类将蕴含普通ITAP。
中文摘要 AI 辅助
我们证明了实秩一单李群乘积中不可约格的非交换拓扑因子定理。约化群C*-代数与边界交叉积之间的中间C*-子代数，恰好是由Furstenberg边界的坐标子乘积产生的交叉积。这一结论源于乘积边界作用的更一般定理，该定理还可得出树版本与混合局部域版本。我们最终表明，$\text{SL}_3(\boldsymbol{Z})$的全旗作用对应的分类，将蕴含普通ITAP。
英文摘要
We prove a noncommutative topological factor theorem for irreducible lattices in products of real rank-one simple Lie groups. The intermediate C*-subalgebras between the reduced group C*-algebra and the boundary crossed product are exactly the crossed products arising from coordinate subproducts of the Furstenberg boundary. This follows from a more general theorem for product boundary actions, which also yields tree and mixed local-field versions. We finally show that, for lattices in connected semisimple real Lie groups with finite center and no compact factors, the scalar-expectation case of the corresponding classification is equivalent to ordinary ITAP.
发表机构
- École normale supérieure（巴黎高等师范学院）
- Université Paris-Saclay（巴黎萨克雷大学）
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