Polyubles, Poisson homogeneous spaces and multi-flag varieties
Shaoqiang Deng, Chuangchuang Kang, Shizhuo Yu

TL;DR
This paper explores the structure of polyubles of Manin triples, establishing isomorphisms and constructing Poisson homogeneous spaces and multi-flag varieties, advancing understanding in Poisson geometry and Lie theory.
Contribution
It introduces a unique isomorphism between polyubles of different orders and constructs classes of Poisson homogeneous spaces and global isomorphisms for multi-flag varieties.
Findings
Established a unique isomorphism between polyubles of different orders.
Constructed classes of Poisson homogeneous spaces and homeomorphisms.
Applied results to multi-flag and multi-double flag varieties, creating global Poisson isomorphisms.
Abstract
A polyuble of a Manin triple can be regarded as the ``-th power'' of it, which plays an important rule in the study of Poisson geometry, mathematical physics and Lie theory. In this paper, we first construct an isomorphism between the -ble and the -ubles of -uble by colored graph and point out it is unique. Then, we construct a class of Poisson homogeneous spaces and obtain a class of Poisson homeomorphisms between them based on the first main result. Last, we apply first two main results to multi-flag varieties as well as multi-double flag varieties and construct a class of global Poisson isomorphisms between them as well as their -leaves.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Advanced Algebra and Geometry
