Résumé : We present some bialgebras and their monoid of characters. We entend the well-known theorem (when the scalars form a field) about linear independence of characters to the case of some rings. Examples of algebraic independence of subfamilies and identites derived from their groups (or monoids) of characters are provided. In this framework, we give a way to factorise characters (the MRS factorisation) as a resolution of unity as well as combinatorial counterparts of this resolution in terms of bases in duality.
Joint work with Darij Grinberg (Drexel University, Philadelphia, US / currently Germany) and Hoang Ngoc Minh (LIPN, Paris XIII University)
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