Cluster倾斜子范畴导出的Abel范畴的recollement和thick子范畴

Recollement and thick subcateories of abelian categories induced by cluster-tilting subcategories

设T是三角范畴D的cluster倾斜子范畴.首先,如果D具有一个关于三角范畴D′和D″的recollement,且满足i*i*(T)T,j*j*(T)T,则给出了这个recollement诱导Abel范畴D/T关于Abel范畴D′/(i*T)和D″/(j*T)的recollement的充分必要条件;其次,如果H是D的thick子范畴,i*表示自然嵌入函子i*:H→D的左伴随函子,且i*TT,那么Abel范畴A′=H/(i*T)是Abel范畴A=D/T的thick子范畴.

Let T be a cluster-tilting subcategory of triangulated category D . Firstly , if D admits a recollement relative to D′ and D″ ,Tsatisfies i＊ i＊（T）T,j＊j＊（T）T,a necessary and sufficient condition for that D/T admits a recollement relative to D′/（i＊T） and D″/（j＊T） was proved .Then ,it was shown that A′= H/（i＊T） is a thick subcategory of A= D/T ,where His a thick subcategory of D,i＊is the left adjoint functor of the natural embedding functor i＊：H→D and T satisfies i＊TT.