Polymultiplicative maps associated with the algebra of iterated Laurent series and the higher-dimensional Contou-Carrere symbol

We study functorial polymultiplicative maps from the multiplicative group of the algebra of n-times iterated Laurent series over a commutative ring in $n+1$ variables into the multiplicative group of the ring. It is proved that if such a map is invariant under continuous automorphisms of this algebra, then it coincides, up to a sign, with an integer power of the n-dimensional Contou-Carrère symbol. Bibliography: 19 titles.