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arXiv · 1510.05282

Dual pairs of quantum moment maps and doubles of Hopf algebras

Gus Schrader·Alexander Shapiro
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Abstract

For any finite-dimensional Hopf algebra $A$ there exists a natural associative algebra homomorphism $D(A) \to H(A)$ between its Drinfeld double $D(A)$ and its Heisenberg double $H(A)$. We construct this homomorphism using a pair of commuting quantum moment maps, and then use it to provide a homomorphism of certain reflection equation algebras. We also explain how the quantization of the Grothendieck-Springer resolution arises in this context.

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Gus Schrader, Alexander Shapiro. 2015-10-18. Dual pairs of quantum moment maps and doubles of Hopf algebras. https://arxiv.org/abs/1510.05282

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