Appears in collection : Combinatorics and Arithmetic for Physics: special days 2023

Lazard elimination (LE) theorems provide uniform formulas for every alphabet (of arbitrary cardinality) and have similar schemes for groups, monoids, Lie algebras and unital associative algebras. This tool gives rise to many implementable algorithms.

We will start from the most celebrated form of LE i.e. on the category of k-Lie algebras (k being a unitary ring), concentrate on monoids and Lie algebras and provide examples on iterated smash-products, where the “rewriting on words” (string rewriting) plays a crucial rˆole to understand the normal forms and how one converges to them.

If times permits we will give other applications of word indexing to hyperlogarithms and character theory.

Based on joint works with Vu Nguyen Dinh.