Fusion in the entwined category of Yetter--Drinfeld modules of a rank-1 Nichols algebra

Details Fusion in the entwined category of Yetter--Drinfeld modules of a rank-1 Nichols algebra Fusion in the entwined category of Yetter--Drinfeld modules of a rank-1 Nichols algebra

2011-09-27

arxiv.org/abs/1109.5919v3

Mathematics

Quantum Algebra

36 pages, amsart++, times, xy. V3: references added, an unnecessary assumption removed, plus some minor changes

Scientific paper

We rederive a popular nonsemisimple fusion algebra in the braided context, from a Nichols algebra. Together with the decomposition that we find for the product of simple Yetter-Drinfeld modules, this strongly suggests that the relevant Nichols algebra furnishes an equivalence with the triplet W-algebra in the (p,1) logarithmic models of conformal field theory. For this, the category of Yetter-Drinfeld modules is to be regarded as an \textit{entwined} category (the one with monodromy, but not with braiding).

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