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Title
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Localizations and sheaves of glider representations
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Author
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Abstract
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| 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 non-commutative geometry we allow schemes over non-commutative 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 (W) under bar (R) in terms of a non-commutative Grothendieck topology based on words of Ore set localizations. (C) 2018 Elsevier B.V. All rights reserved. |
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Language
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English
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Source (journal)
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Journal of pure and applied algebra. - Amsterdam
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Publication
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Amsterdam
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2019
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ISSN
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0022-4049
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DOI
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10.1016/J.JPAA.2018.09.012
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Volume/pages
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223
:6
(2019)
, p. 2635-2672
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ISI
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000457668600018
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Full text (Publisher's DOI)
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Full text (publisher's version - intranet only)
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