On the structure of irreducible Yetter-Drinfeld modules over $ D $

Abstract

A class of algebras $ D(m, d, \xi) $ introduced by ^{[<span class="xref"><a href="#b22" ref-type="bibr">22</a></span>]} were not pointed and generated by the coradical of $ D(m, d, \xi) $. Let $ D $ be the quotient of $ D(m, d, \xi) $ module the principle ideal $ (g^m-1) $. First, we describe all simple left modules of $ D $. Then, according to Radford's method, we construct the Yetter-Drinfeld module over $ D $ by the tensor product of a simple module of $ D $ and $ D $ itself. Hence, we find some simple left Yetter-Drinfeld modules over $ D $, and the relevant braidings are of a triangular type.