Growth of structure constants of free Lie algebras relative to Hall bases
Karine Beauchard,
Jérémy Le Borgne,
Frédéric Marbach
Abstract:We derive a priori bounds on the size of the structure constants of the free Lie algebra over a set of indeterminates, relative to its Hall bases. We investigate their asymptotic growth, especially as a function of the length of the involved Lie brackets.First, using the classical recursive decomposition algorithm, we obtain a rough upper bound valid for all Hall bases. We then introduce new notions (which we call alphabetic subsets and relative foldings) related to structural properties of the Lie brackets cr… Show more
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