Algebra & Number Theory

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

Oliver Braunling

Full-text: Open access

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
Received: 16 June 2012
Revised: 14 April 2013
Accepted: 9 September 2013
First available in Project Euclid: 20 December 2017

Permanent link to this document
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

Subjects
Primary: 17B56: Cohomology of Lie (super)algebras 17B67: Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
Secondary: 32A27: Local theory of residues [See also 32C30]

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

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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References

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