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The \(R\)-matrix action of untwisted affine quantum groups at roots of 1 - MaRDI portal

The \(R\)-matrix action of untwisted affine quantum groups at roots of 1 (Q1840469)

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The \(R\)-matrix action of untwisted affine quantum groups at roots of 1
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    The \(R\)-matrix action of untwisted affine quantum groups at roots of 1 (English)
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    22 January 2002
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    Let \(\widehat{\mathfrak g}\) be an untwisted affine Kac-Moody algebra. The author proves that the unrestricted specializations of \(U_q(\widehat{\mathfrak g})\) at odd roots of 1 are braided Hopf algebras. In particular, specializing \(q\) at 1, the function algebra \(F[\widehat{H}]\) of the Poisson algebraic group \(\widehat{H}\), dual of a Kac-Moody group \(\widehat{G}\) with Lie algebra \(\widehat{\mathfrak g}\), is braided. This implies that the action of the universal \(R\)-matrix on tensor products of Verma modules can be specialized at odd roots of 1.
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    Kac-Moody algebra
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    braided Hopf algebra
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    quantized universal enveloping algebra
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    Poisson proalgebraic group
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    \(R\)-matrix
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    Verma module
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