Galois G-covering of quotients of linear categories |
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| Institution: | 1. Department of Mathematical Sciences, Tsinghua University, 100084 Beijing, PR China;2. School of Mathematics and Statistics, Changsha University of Science and Technology, 410114 Changsha, Hunan, PR China;1. Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, México D.F. 04510, Mexico;2. Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, México D.F. 04510, Mexico;3. Université de Paris et Sorbonne Université, CNRS, IMJ-PRG, Bâtiment Sophie Germain, 5 rue Thomas Mann, 75205 Paris Cedex 13, France;1. Department of Mathematics, University of Colorado, Colorado Springs, CO 80918-3733, USA;2. Department of Mathematics, University of Hawaii, Hilo, 200 W. Kawili St., Hilo, HI, 96720-4091, USA;1. Department of Mathematics, Lehigh University, Bethlehem, PA 18015, USA;2. Mathematics Institute, Zeeman Building, Coventry CV4 7AL, UK;1. Institute of Mathematics, Faculty of Mechanical Engineering, Brno University of Technology, Brno, Czech Republic;2. Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Brno, Czech Republic;3. Radix Trading LLC, Chicago, IL, USA;1. School of Mathematics and Statistics, Northwestern Polytechnical University, Xi''an, Shaanxi 710072, PR China;2. Department of Mathematics, University of Wisconsin-Whitewater, 800 W. Main Street, Whitewater, WI 53190, USA;3. School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, PR China;4. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, PR China |
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| Abstract: | In this paper, we introduce the notion of G-liftable ideals, which extends the liftable ideas defined by Assem and Le Meur. We characterize the G-liftable ideals and construct the Galois G-coverings of quotients of categories associated to the G-liftable ideals. In particular, we study the behavior of G-liftable admissible ideals under Galois G-coverings. Furthermore, we show that the ideals generated by finite dimensional projective modules over a locally bounded linear categories are admissible G-liftable ideals. As an application, we provide a reduction technique for dealing with the existence of Serre functors in the stable categories of Gorenstein projective objects. |
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| Keywords: | Admissible ideal Quotient of linear category |
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