Localizations for construction of quantum coset spaces

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dc.creatorSkoda, Zoran
dc.date2003-01-09
dc.date.accessioned2026-07-07T07:48:44Z
dc.date.available2026-07-07T07:48:44Z
dc.descriptionViewing comodule algebras as the noncommutative analogues of affine varieties with affine group actions, we propose rudiments of a localization approach to nonaffine Hopf algebraic quotients of noncommutative affine varieties corresponding to comodule algebras. After reviewing basic background on noncommutative localizations, we introduce localizations compatible with coactions. Coinvariants of these localized coactions give local information about quotients. We define Zariski locally trivial quantum group algebraic principal and associated bundles. Compatible localizations induce localizations on the categories of Hopf modules. Their interplay with the functor of taking coinvariants and its left adjoint is stressed out. Using localization approach, we constructed a natural class of examples of quantum coset spaces, related to the quantum flag varieties of type A of other authors. Noncommutative Gauss decomposition via quasideterminants reveals a new structure in noncommutative matrix bialgebras. Particularily, in the "quantum" case, calculations with quantum minors yield the structure theorems.
dc.description34 pages bcp.sty; talk at the conference "Noncommutative geometry and quantum groups", Warszaw Sep 15-29, 2001; to appear in Banach Institute Publications
dc.identifierhttps://arxiv.org/abs/math/0301090
dc.identifierhttp://arxiv.org/abs/math/0301090
dc.identifierBanach Center Publ. 61 (2003) 265-298
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/124605
dc.subjectQuantum Algebra
dc.subjectHigh Energy Physics - Theory
dc.subjectAlgebraic Geometry
dc.subject14A22, 16W30,14L30,58B32
dc.titleLocalizations for construction of quantum coset spaces
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