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bibkey: jiacapel2024genericlielength
authors: Yifan Jia; Angela Capel
year: 2024
title: A generic quantum Wielandt's inequality
doi: 10.22331/q-2024-05-02-1331
url: https://arxiv.org/abs/2301.08241
claim: "Conjecture 6 asks whether a random Lie-generating set of su(n) has Lie-length Theta(log n) almost surely."
strata_touched:
  - D5/S3/Quantum/Algebra/GenericLieLength
license: citation-only
triage: anchor

Verified locator

DOI: https://doi.org/10.22331/q-2024-05-02-1331

Source: https://arxiv.org/abs/2301.08241

Source statements

Definition 3 (arXiv v3, p. 17) states: “The Lie-length of a Lie-generating system $U$ of a finite-dimensional Lie-algebra $\mathcal{A}$ is the minimal length of the (right-nested) brackets such that the brackets span the whole Lie-algebra, namely $\mathtt{Lie}\ell (U)=\min \{\ell \mid \mathcal{A}=\mathrm{span}\{U_n,n\le \ell \}\}$, where $U_n$ is defined as: $U_1=\mathrm{span}\{U\};U_n=\mathrm{span}[U,U_{n-1}]$, $n\ge 2$.”

Conjecture 6 (arXiv v3, p. 19) states: “Let $S$ be a random Lie-generating set of $\mathfrak{su}(n)$, then $\mathtt{Lie}\ell (S)=\Theta (\log n)$ almost surely.”