We describe a Nichols-algebra-motivated construction of an octuplet chiral algebra that is a W_3-counterpart of the triplet algebra of (p,1) logarithmic models of two-dimensional conformal field theory.
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 algebr
a 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).
A Virasoro central charge can be associated with each Nichols algebra with diagonal braiding in a way that is invariant under the Weyl groupoid action. The central charge takes very suggestive values for some items in Heckenbergers list of rank-2 Nic
hols algebras. In particular, this might be viewed as an indication of the existence of reasonable logarithmic extensions of W_3==WA_2, WB_2, and WG_2 models of conformal field theory. In the W_3 case, the construction of an octuplet extended algebra---a counterpart of the triplet (1,p) algebra---is outlined.
