Finite-dimensional Nichols algebras over dual Radford algebras

Abstract

For n, m ∈ N, let Hn,m be the dual of the Radford algebra of dimension n 2m. We present new finite-dimensional Nichols algebras arising from the study of simple Yetter-Drinfeld modules over Hn,m. Along the way, we describe the simple objects in Hn,m Hn,m YD and their projective envelopes. Then, we determine those simple modules that give rise to finite-dimensional Nichols algebras for the case n = 2. There are 18 possible cases. We present by generators and relations the corresponding Nichols algebras on five of these eighteen cases. As an application, we characterize finite-dimensional Nichols algebras over indecomposable modules for n = 2 = m and n = 2, m = 3, which recovers some results of the second and third author in the former case, and of Xiong in the latter.