# Localizations for construction of quantum coset spaces

@article{Skoda2003LocalizationsFC,
title={Localizations for construction of quantum coset spaces},
author={Zoran Skoda},
journal={Banach Center Publications},
year={2003},
volume={61},
pages={265-298}
}
• Z. Skoda
• Published 9 January 2003
• Mathematics
• Banach Center Publications
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…
30 Citations
Noncommutative localization in noncommutative geometry
The aim of these notes is to collect and motivate the basic localization toolbox for the geometric study of spaces'', locally described by noncommutative rings and their categories of one-sided
Categorified symmetries
• Mathematics
• 2009
Quantum field theory allows more general symmetries than groups and Lie algebras. For instance quantum groups, that is Hopf algebras, have been familiar to theoretical physicists for a while now.
Differential Calculi on Quantum Principal Bundles over Projective Bases
• Mathematics
• 2021
We propose a sheaf-theoretic approach to the theory of differential calculi on quantum principal bundles over non-affine bases. Our main class of examples is given by quantum principal bundles over
2 00 6 Every quantum minor generates an Ore set
The subset multiplicatively generated by any given set of quantum minors and the unit element in the quantum matrix bialgebra satisfies the left and right Ore conditions. Quantum matrix groups ([9,
Every quantum minor generates an Ore set
The subset multiplicatively generated by any given set of quantum minors and the unit element in the quantum matrix bialgebra satisfies the left and right Ore conditions. Quantum matrix groups ([9,
2 8 N ov 2 00 8 Some equivariant constructions in noncommutative algebraic geometry
Philosophy of quantum groups as Hopf algebras and their actions and coactions on algebras and graded algebras captures only affine and some projective phenomena in noncommutative algebraic geometry.
Compatibility of (co)actions and localizations
Earlier, Lunts and Rosenberg studied a notion of compatibility of endofunctors with localization functors, with an application to the study of differential operators on noncommutative rings and
\v{C}ech cocycles for quantum principal bundles
In other to study connections and gauge theories on noncommutative spaces it is useful to use the local trivializations of principal bundles. In this note we show how to use noncommutative
Some equivariant constructions in noncommutative algebraic geometry
We here present rudiments of an approach to geometric actions in noncommutative algebraic geometry, based on geometrically admissible actions of monoidal categories. This generalizes the usual
Some Equivariant Constructions in Noncommutative Algebraic Geometry
Abstract We here present rudiments of an approach to geometric actions in noncommutative algebraic geometry, based on geometrically admissible actions of monoidal categories. This generalizes the

## References

SHOWING 1-10 OF 131 REFERENCES
Semiquantum geometry
• Mathematics
• 1996
In this paper we study associative algebras with a Poisson algebra structure on the center acting by derivations on the rest of the algebra. These structures appeared in the study of quantum groups
Module and Comodule Categories-a Survey
The theory of modules over associative algebras and the theory of comodules for coassociative coalgebras were developed fairly independently during the last decades. In this survey we display an
Principal homogeneous spaces for arbitrary Hopf algebras
LetH be a Hopf algebra over a field with bijective antipode,A a rightH-comodule algebra,B the subalgebra ofH-coinvariant elements and can:A ⊗BA →A ⊗H the canonical map. ThenA is a faithfully flat (as
Coherent states for quantum compact groups
• Mathematics
• 1994
Coherent states are introduced and their properties are discussed for simple quantum compact groupsAl, Bl, Cl andDl. The multiplicative form of the canonical element for the quantum double is used to
Noncommutative smooth spaces
• Mathematics
• 2000
We will work in the category Al gk of associative unital algebras over a fixed base field k. If A € Ob(Algk), we denote by 1A € A the unit in A and by m A : A ⊗ A—→A the product. For an algebra A, we
Quantum Grassmann manifolds
AbstractOrbits of the quantum dressing transformation forSUq(N) acting on its solvable dual are introduced. The case is considered when the corresponding classical orbits coincide with Grassmann
Strong connections on quantum principal bundles
A gauge invariant notion of a strong connection is presented and characterized. It is then used to justify the way in which a global curvature form is defined. Strong connections are interpreted as
A Locally Trivial Quantum Hopf Fibration
• Mathematics
• 2001
Abstract The irreducible *-representations of the polynomial algebra $\mathcal{O}(S^{3}_{pq})$ of the quantum3-sphere introduced by Calow and Matthes are classified. The K-groups of its universal
Cohomology of Schematic Algebras
• Mathematics
• 1996
LetRbe a positively graded Noetheriank-algebra and let Proj R=(R, κ+)−grbe the quotient category of the category of gradedR-modulesR−grmodulo those of finite length. IfRis schematic (cf. [F. Van