Loop groups \(SL_{2}(F[X;X^{ - 1}])\), universal central extensions and additive Steinberg symbols (Q436070)
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scientific article; zbMATH DE number 6060703
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Loop groups \(SL_{2}(F[X;X^{ - 1}])\), universal central extensions and additive Steinberg symbols |
scientific article; zbMATH DE number 6060703 |
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Loop groups \(SL_{2}(F[X;X^{ - 1}])\), universal central extensions and additive Steinberg symbols (English)
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28 July 2012
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universal central extension
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presentation
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loop group
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Schur multiplier
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Tits system
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additive Steinberg symbols
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Let \textbf{F} be a field with more than four elements. The author constructs a presentation of the universal central extension \(\widehat{St}_2(\mathbf{F}[X,X^{-1}])\) of \(SL_2(\mathbf{F}[X,X^{-1}])\). In this presentation one has central elements \(\hat\theta_\pm(t,t')=\hat x_\pm (t)\hat x_\pm (t')\hat x_\pm (t+t')^{-1}\). The author calls them additive Steinberg symbols.NEWLINENEWLINEFrom the Tits system of affine \(A_1\) type on \(SL_2(\mathbf{F}[X,X^{-1}])\) he obtains such a Tits system on \(\widehat{St}_2(\mathbf{F}[X,X^{-1}])\).
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