Higher-dimensional Contou-Carrère symbol and continuous automorphisms

We prove that the higher-dimensional Contou-Carrère symbol is invariant under continuous automorphisms of algebras of iterated Laurent series over a ring. Applying this property, we obtain a new explicit formula for the higher-dimensional Contou-Carrère symbol. Unlike previously known formulas, this formula is given over an arbitrary ring, not necessarily a $\mathbb Q$-algebra, and does not involve algebraic $K$-theory.

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