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arXiv · 1206.2025

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

Oliver Braunling
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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.

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BibTeXRIS

Oliver Braunling. 2014-02-05. Adele residue symbol and Tate's central extension for multiloop Lie algebras. https://doi.org/10.2140/ant.2014.8.19

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