## Algebra & Number Theory

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

Oliver Braunling

#### 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.

#### Article information

Source
Algebra Number Theory, Volume 8, Number 1 (2014), 19-52.

Dates
Revised: 14 April 2013
Accepted: 9 September 2013
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.ant/1513730133

Digital Object Identifier
doi:10.2140/ant.2014.8.19

Mathematical Reviews number (MathSciNet)
MR3207578

Zentralblatt MATH identifier
1371.17019

#### Citation

Braunling, Oliver. Adèle residue symbol and Tate's central extension for multiloop Lie algebras. Algebra Number Theory 8 (2014), no. 1, 19--52. doi:10.2140/ant.2014.8.19. https://projecteuclid.org/euclid.ant/1513730133

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