Redundancy rank of non-compact semisimple Lie groups

Prove that the redundancy rank ρ(G) is infinite for every non-compact semisimple Lie group G.

Background

The redundancy rank ρ(G) is the minimal m such that any generating n-tuple with n > m is redundant. The paper computes ρ(G) for connected abelian Lie groups and discusses reductions for general connected Lie groups.

Minsky’s work shows that ρ(G) is infinite for SL_2(R) and SL_2(C), prompting the authors to propose a broader conjecture for all non-compact semisimple Lie groups.