On the representation theory of the Drinfeld double of the Fomin-Kirillov algebra $\mathcal{FK}_3$

Abstract

Let $\mathcal{D}$ be the Drinfeld double of $\mathcal{FK}_3\#\Bbbk{\mathbb S}_3$. The simple $\mathcal{D}$-modules were described in arXiv:1409.0438. In the present work, we describe the indecomposable summands of the tensor product between them. We classify the extensions of the simple modules and show that $\mathcal{D}$ is of wild representation type. We also investigate the projective modules and their tensor products.