arXiv subjects
Publications and source records attributed to B. Greenfeld.
We give a short construction refuting the Köthe Conjecture. The construction is based on the point module approach to the problem, introduced by the first-named and second-named authors together with Easton and Ford.
Nichols algebras are among the most important and mysterious objects in quantum algebra. We continue the systematic program of studying them through their point modules. We study truncated point modules of Nichols algebras associated with racks and 2-cocycles over non-abelian groups. We determine the truncated point spaces for all currently known finite-dimensional Nichols algebras arising from simple Yetter-Drinfeld modules over groups. In particular, for all such algebras the space of 3-truncated point modules is empty. We further find all truncated point modules for other important families, including affine racks equipped with the constant 2-cocycle -1, and for the non-trivial indecomposable rack of size three with the constant 2-cocycle a cubic root of one.