2013/02/28 by Gustavo Jasso · 3 citations
Mathematics · #Advanced Combinatorial Mathematics #Algebra over a field #Algebraic structures and combinatorial models #Bijection #Class (philosophy) #Homotopy and Cohomology in Algebraic Topology #Point (geometry) #Reduction (mathematics) #Torsion (gastropod) #math.RT #msc:16G10
paper · pdf · doi:10.1093/imrn/rnu163
published as Int. Math. Res. Not. IMRN (16) (2015): 7190-7237 · 32 pages. Shortened abstract, corrected typos in references [1] and [9]
arxiv created 2014/03/27 · openalex publication_date 2014/09/26 · openalex created_date 2016/06/24 · arxiv updated 2017/06/15 · openalex updated_date 2026/08/05
The class of support |τ|-tilting modules was introduced recently by Adachi et al. These modules complete the class of tilting modules from the point of view of mutations. Given a finite-dimensional algebra |A|, we study all basic support |τ|-tilting |A|-modules which have a given basic |τ|-rigid |A|-module as a direct summand. We show that there exist an algebra |C| such that there exists an order-preserving bijection between these modules and all basic support |τ|-tilting |C|-modules; we call this passage |τ|-tilting reduction. An important step in our proof is the formation of |τ|-perpendicular categories which are analogs of ordinary perpendicular categories. Finally, we show that |τ|-tilting reduction is compatible with silting reduction and 2-Calabi–Yau reduction in appropriate triangulated categories.