On the Steinberg property of the Contou-Carrere symbol

英文摘要：

The aim of this work is to show that the Contou-Carrère symbol satisfies the property of Steinberg symbols: $<f,1-f>_{A((t))^\times} = 1$ for all elements $f,1-f \in A((t))^\times$. Moreover, we offer a cohomological characterization of the Contou-Carrère symbol from the commutator of a central extension of groups.