Celebratio Mathematica — Benkart

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G. Benkart, M. Pereira, and S. Witherspoon: “Yetter–Drinfeld modules under cocycle twists,” J. Algebra 324 : 11 (December 2010), pp. 2990–3006. To Susan Montgomery in honor of her distinguished career. MR 2732983 Zbl 1223.16011 ArXiv 0908.1563 article

We give an explicit formula for the correspondence between simple Yetter–Drinfeld modules for certain finite-dimensional pointed Hopf algebras \( H \) and those for cocycle twists \( H^{\sigma} \) of \( H \). This implies an equivalence between modules for their Drinfeld doubles. To illustrate our results, we consider the restricted two-parameter quantum groups \( \mathfrak{u}_{r,s}(\mathfrak{sl}_n) \) under conditions on the parameters guaranteeing that \( \mathfrak{u}_{r,s}(\mathfrak{sl}_n) \) is a Drinfeld double of its Borel subalgebra. We determine explicit correspondences between \( \mathfrak{u}_{r,s}(\mathfrak{sl}_n) \)-modules for different values of \( r \) and \( s \) and provide examples where no such correspondence can exist. Our examples were obtained via the computer algebra system SINGULAR::PLURAL.

Susan Montgomery	Related
Mariana Pereira	Related
Sarah J. Witherspoon	Related