2016/02/17 by Frederik Caenepeel, Caenepeel, Frederik, F. Van Oystaeyen +2
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA) #math.RA
paper · pdf · doi:10.48550/arxiv.1602.05338
32 pages
openalex publication_date 2016/02/17 · arxiv created 2016/07/15 · arxiv updated 2016/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The notion of a glider representation of a chain of normal subgroups of a group is defined by a new structure, i.e. a fragment for a suitable filtration on the group ring. This is a special case of general glider representations defined for a positively filtered ring R with filtration FR and subring S = F0R. Nice examples appear for chains of groups, chains of Lie algebras, rings of differential operators on some variety or V-gliders for W for algebraic varieties V and W. This paper aims to develop a scheme theory for glider representations via the localizations of filtered modules. With an eye to noncommutative geometry we allow schemes over noncommutative rings with particular attention to so-called almost commutative rings. We consider particular cases of Proj~ R (e.g. for some P.I. ring R) in terms of prime ideals, R-tors in terms of torsion theories and \underlineW(R) in terms of a noncommutative Grothendieck topology based on words of Ore set localizations.