2010/06/07 by Dong Yang, Yang, Dong
Mathematics · Physics and Astronomy · #16E45 #18E30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT) #math.CT #math.RT #msc:16E45 #msc:18E30
paper · pdf · doi:10.48550/arxiv.1006.1227
10 pages. a few mistakes corrected. To appear in P.A.M.S
openalex publication_date 2010/06/07 · arxiv created 2010/11/17 · arxiv updated 2010/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \ca be a small dg category over a field k and let \cu be a small full subcategory of the derived category \cd\ca which generate all free dg \ca-modules. Let (\cb,X) be a standard lift of \cu. We show that there is a recollement such that its middle term is \cd\cb, its right term is \cd\ca, and the three functors on its right side are constructed from X. This applies to the pair (A,T), where A is a k-algebra and T is a good n-tilting module, and we obtain a result of Bazzoni--Mantese--Tonolo. This also applies to the pair (\ca,\cu), where \ca is an augmented dg category and \cu is the category of `simple' modules, e.g. \ca is a finite-dimensional algebra or the Kontsevich--Soibelman A_∞-category associated to a quiver with potential.