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arXiv · 0706.0243

Braided doubles

Yuri Bazlov·Arkady Berenstein
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Abstract

Braided doubles provide a unifying framework for classical and quantum universal enveloping algebras and rational Cherednik algebras. They are a class of algebras with triangular decomposition, arising from a deformation problem, the solutions to which are called quasi-Yetter-Drinfeld modules. A basic family of quasi-YD modules is provided by braidings (matrices satisfying the quantum Yang-Baxter equation); these give rise to quantum versions of the Weyl algebra, where the role of polynomial rings is played by Nichols-Woronowicz algebras. Rational Cherednik algebras for t = 0 emerge as subalgebras in doubles of Nichols-Woronowicz algebras. For nonzero t, the Nichols-Woronowicz algebra is replaced with an algebra associated to the classical Yang-Baxter equation.

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Yuri Bazlov, Arkady Berenstein. 2011-11-23. Braided doubles. https://arxiv.org/abs/0706.0243

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