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Limit properties of quantum twists at q->1, from semi-classical twists to noncommutative geometry

Maxim Samsonov
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Abstract

A problem of defining the quantum analogues for semi-classical twists in $U(\mathfrak{g})[[t]]$ is considered. First, we study specialization at $q=1$ of singular coboundary twists defined in $U_{q}(\mathfrak{g})[[t]]$ for $\mathfrak{g}$ being a nonexceptional Lie algebra, then we consider specialization of noncoboundary twists when $\mathfrak{g}=\mathfrak{sl}_{3}$ and obtain $q-$deformation of the semi-classical twist introduced by Connes and Moscovici in noncommutative geometry.

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Maxim Samsonov. 2005-05-02. Limit properties of quantum twists at q->1, from semi-classical twists to noncommutative geometry. https://arxiv.org/abs/math/0309311

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