We first prove that the subcategory of fixed points of mutation determined by an excep- tional object E in a triangulated category coincide with the perpendicular category of E. Based on this characterisation, we prov...We first prove that the subcategory of fixed points of mutation determined by an excep- tional object E in a triangulated category coincide with the perpendicular category of E. Based on this characterisation, we prove that the subcategory of fixed points of mutation in the derived category of the coherent sheaves on weighted projective line with genus one is equivalent to the derived category of a hereditary algebra. Meanwhile, we induce two new recollements by left and right mutations from a given recollement.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.11126268,11071040)Science and Technology Development Fund of Fuzhou University(Grant No.2011-xq-22)
文摘We first prove that the subcategory of fixed points of mutation determined by an excep- tional object E in a triangulated category coincide with the perpendicular category of E. Based on this characterisation, we prove that the subcategory of fixed points of mutation in the derived category of the coherent sheaves on weighted projective line with genus one is equivalent to the derived category of a hereditary algebra. Meanwhile, we induce two new recollements by left and right mutations from a given recollement.
