An effective Lie–Kolchin Theorem for quasi-unipotent matrices

Thomas Koberda, Feng Luo, Hongbin Sun

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We establish an effective version of the classical Lie–Kolchin Theorem. Namely, let A,B∈GLm(C) be quasi-unipotent matrices such that the Jordan Canonical Form of B consists of a single block, and suppose that for all k⩾0 the matrix ABk is also quasi-unipotent. Then A and B have a common eigenvector. In particular, 〈A,B〉<GLm(C) is a solvable subgroup. We give applications of this result to the representation theory of mapping class groups of orientable surfaces.

Original languageEnglish (US)
Pages (from-to)304-323
Number of pages20
JournalLinear Algebra and Its Applications
StatePublished - Nov 15 2019

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


  • Lie–Kolchin theorem
  • Mapping class groups
  • Solvable groups
  • Unipotent matrices


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