Adèle residue symbol and Tate’s central extension for multiloop Lie algebras

Braunling, Oliver

doi:10.2140/ant.2014.8.19

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

Oliver Braunling

Vol. 8 (2014), No. 1, 19–52

DOI: 10.2140/ant.2014.8.19

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 to some extent. 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.

Keywords

adèle, residue symbol, Tate central extension, Kac–Moody, Japanese group

Mathematical Subject Classification 2010

Primary: 17B56, 17B67

Secondary: 32A27

Milestones

Received: 16 June 2012

Revised: 14 April 2013

Accepted: 9 September 2013

Published: 20 April 2014

Authors

Oliver Braunling
Fakultät für Mathematik Universität Duisburg-Essen Thea-Leymann-Straße 9 45127 Essen Germany
http://www.esaga.uni-due.de/oliver.braeunling/

Vol. 8, No. 1, 2014