Mutation matrices from Poisson CGL extensions

Zihang Liu; Jiang-Hua Lu; Yipeng Mi

Mutation matrices from Poisson CGL extensions

Rings and Algebras 2026-07-08 v1 Symplectic Geometry

Authors: Zihang Liu , Jiang-Hua Lu , Yipeng Mi

Abstract

Symmetric Poisson CGL extensions form a particular class of polynomial Poisson algebras that are shown by K. Goodearl and M. Yakimov to admit compatible cluster structures. In this paper, we give explicit formulas for a family of mutation matrices in the Goodearl-Yakimov theory via matrix products as well as by entry-wise description.

Cite

@article{arxiv.2607.07028,
  title  = {Mutation matrices from Poisson CGL extensions},
  author = {Zihang Liu and Jiang-Hua Lu and Yipeng Mi},
  journal= {arXiv preprint arXiv:2607.07028},
  year   = {2026}
}