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This paper demonstrates diameter bounds related to Babai's conjecture for finite simple Lie algebras, indicating important relationships between algebra types.
We prove strong and explicit diameter bounds for finite simple Lie algebras, which parallel Babai's conjecture for finite simple groups. Specifically, we show that any nonabelian finite simple Lie algebra g over Fₚ has diameter O((log |g|)D) for D ≈ 3.11 with respect to any generating set. For absolutely simple classical Lie algebras over Fₚ, we establish the sharper bound O(log |g|) when the Lie type is fixed and the generators are chosen uniformly at random.
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Barbieri et al. (2025) studied this question.
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