https://hal-univ-artois.archives-ouvertes.fr/hal-02942576Calmès, BaptisteBaptisteCalmèsLML - Laboratoire de Mathématiques de Lens - UA - Université d'ArtoisZainoulline, KirillKirillZainoullineZhong, ChanglongChanglongZhongFormal affine Demazure and Hecke algebras of Kac-Moody root systemsHAL CCSD2020[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG]Calmès, Baptiste2020-09-18 09:31:532021-11-03 06:19:252020-09-18 09:31:53enPreprints, Working Papers, ...1We define the formal affine Demazure algebra and formal affine Hecke algebra associated to a Kac-Moody root system. We prove the structure theorems of these algebras, hence, extending several result and construction (presentation in terms of generators and relations, coproduct and product structures, filtration by codimension of Bott-Samelson classes, root polynomials and multiplication formulas) that were previously known for finite root system.