Centralisers of Formal Maps
Anthony G. O’Farrell · Mathematical Proceedings of the Royal Irish Academy · 2022
We consider the formal maps in any finite dimension d with coefficients in an integral domain K with identity.Those invertible under formal composition form a group G.We consider the centraliser C g of an element g ∈ G which has infinite order and is tangent to the identity of G.If g has infinite order and K is a field of characteristic zero we show that C g contains an isomorphic copy of the additive group (K, +).If g has infinite order and K has positive characteristic we show that C g contains an uncountable abelian subgroup.The proofs are quite different in finite characteristic and in characteristic zero, but are connected by so-called sum functions.