Définition abstraite dʹun système de racines dans le cas symétrisable

This paper presents an axiomatic description in a base free way of infinite root systems as those found in the study of Kac–Moody–Borcherdsʹ algebras. In 1979, R. Moody [Adv. Math. 33 (1979) 144] posed the problem of finding such a description. In [Comm. Algebra 23 (1995) 4791], J.G. Bliss has already presented two answers to this question with his notions of “geometric root systems” and “rational root systems.” This new answer to Moodyʹs question fits into the framework of the earlier axiomatic theory of the « systèmes générateurs de racines » developed in [N. Bardy, Mém. Soc. Math. Fr. (N.S.) 65 (1996)].