Localizations for construction of quantum coset spaces

Zoran Škoda. "Localizations for construction of quantum coset spaces." Banach Center Publications 61.1 (2003): 265-298. <http://eudml.org/doc/281851>.

@article{ZoranŠkoda2003,
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 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 the localization approach, we construct 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. In the quantum case, calculations with quantum minors yield structure theorems.},
author = {Zoran Škoda},
journal = {Banach Center Publications},
keywords = {Hopf algebra; noncommutative localization; quantum bundle; comodule},
language = {eng},
number = {1},
pages = {265-298},
title = {Localizations for construction of quantum coset spaces},
url = {http://eudml.org/doc/281851},
volume = {61},
year = {2003},
}

TY - JOUR
AU - Zoran Škoda
TI - Localizations for construction of quantum coset spaces
JO - Banach Center Publications
PY - 2003
VL - 61
IS - 1
SP - 265
EP - 298
AB - 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 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 the localization approach, we construct 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. In the quantum case, calculations with quantum minors yield structure theorems.
LA - eng
KW - Hopf algebra; noncommutative localization; quantum bundle; comodule
UR - http://eudml.org/doc/281851
ER -