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

Abstract

Let $\mathcal{D}$ be the Drinfeld double of ${\mathcal{F}\mathcal{K}}_3\#\mathbb{k}{\mathbb{S}}_3$. 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.

23 pages, 4 figures