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arXiv · 1210.3096

Multi-brace cotensor Hopf algebras and quantum groups

Xin Fang·Marc Rosso
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Abstract

We construct multi-brace cotensor Hopf algebras with bosonizations of quantum multi-brace algebras as examples. Quantum quasi-symmetric algebras are then obtained by taking particular initial data; this allows us to realize the whole quantum group associated to a symmetrizable Kac-Moody Lie algebra as a quantum quasi-symmetric algebra and all highest weight irreducible representations can be constructed using this machinery. It also provides a systematic way to construct simple modules over the quantum double of a quantum group.

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Xin Fang, Marc Rosso. 2012-10-11. Multi-brace cotensor Hopf algebras and quantum groups. https://arxiv.org/abs/1210.3096

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