Adele residue symbol and Tate's central extension for multiloop Lie algebras

Abstract

We generalize the linear algebra setting of Tate's central extension to arbitrary dimension. In general, one obtains a Lie (n+1)-cocycle. We compute it explicitly. The construction is based on a Lie algebra variant of Beilinson's adelic multidimensional residue symbol, generalizing Tate's approach to the local residue symbol for 1-forms on curves.

Cited by in corpus (3)

• On the local residue symbol in the style of Tate and Beilinson
• Local Beilinson-Tate Operators
• Hochschild coniveau spectral sequence and the Beilinson residue