On a family of vector space categories. (Q1407200)

The authors study in detail a class of vector space \(K\)-categories \(\mathbb{K}_K=(\mathbb{K},|-|\colon\mathbb{K}\to\text{mod\,}K)\) defined by quivers and relations presented in the paper, where \(K\) is an algebraically closed field. It is shown that the subspace category \({\mathcal U}(\mathbb{K}_K)\) of any such vector space \(K\)-category \(\mathbb{K}_K\) is tame domestic. Moreover, the finite-dimensional indecomposable objects of \({\mathcal U}(\mathbb{K}_K)\) are described and the Auslander-Reiten quiver \(\Gamma({\mathcal U}(\mathbb{K}_K)) \) of the category \({\mathcal U}(\mathbb{K}_K)\) is completely determined. The results are applied in a construction of an interesting class of sincere domestic finite-dimensional algebras of arbitrary large global dimension.