Vol. 8, No. 1, 2014

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ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Adèle residue symbol and Tate's central extension for multiloop Lie algebras

Oliver Braunling

Vol. 8 (2014), No. 1, 19–52

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.

adèle, residue symbol, Tate central extension, Kac–Moody, Japanese group
Mathematical Subject Classification 2010
Primary: 17B56, 17B67
Secondary: 32A27
Received: 16 June 2012
Revised: 14 April 2013
Accepted: 9 September 2013
Published: 20 April 2014
Oliver Braunling
Fakultät für Mathematik
Universität Duisburg-Essen
Thea-Leymann-Straße 9
45127 Essen