Virasoro central charges for Nichols algebras

Abstract

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 Heckenberger's list of rank-2 Nichols 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.

23 pages, amsart++, xy, times. V2: Presentation somewhat streamlined. The results of several specific Weyl transformations corrected

Cited by in corpus (3)

• Rank 2 Nichols Algebras of Diagonal Type over Fields of Positive Characteristic
• Coset construction of logarithmic minimal models: branching rules and branching functions
• Fusion in the entwined category of Yetter--Drinfeld modules of a rank-1 Nichols algebra