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

Abstract

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).

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

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Cited by in corpus (7)

• Lattice fusion rules and logarithmic operator product expansions
• A classification of Nichols algebras of semi-simple Yetter-Drinfeld modules over non-abelian groups
• Logarithmic ^sl(2) CFT models from Nichols algebras. 1
• Representations of ${\bar{U}}_{q}s\ell (2|1)$ at even roots of unity
• Integrable perturbations of conformal field theories and Yetter-Drinfeld modules
• Nichols Algebras and Quantum Principal Bundles
• A note on the "logarithmic-W_3" octuplet algebra and its Nichols algebra