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- W2949597908 abstract "Viewing 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 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 coset spaces, related to the 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 minors yield the structure theorems." @default.
- W2949597908 created "2019-06-27" @default.
- W2949597908 creator A5068178918 @default.
- W2949597908 date "2003-01-09" @default.
- W2949597908 modified "2023-09-26" @default.
- W2949597908 title "Localizations for construction of quantum coset spaces" @default.
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