Related papers: Quantum principal bundles over quantum real projec…
We propose a conceptually economical and computationally tractable completion of the foundations of gauge theory on quantum principal bundles \`{a} la Brzezi\'{n}ski--Majid to the case of general differential calculi and strong bimodule…
Differential calculi are obtained for quantum homogeneous spaces by extending Woronowicz' approach to the present context. Representation theoretical properties of the differential calculi are investigated. Connections on quantum…
In this paper we count the number of isomorphism classes of geometrically indecomposable quasi-parabolic structures of a given type on a given vector bundle on the projective line over a finite field. We give a conjectural cohomological…
In this thesis we study the Durdevic theory of differential calculi on quantum principal bundles within the domain of noncommutative geometry. Throughout the exposition, an algebraic approach based on Hopf algebras is employed. We begin by…
We study the spaces of stable real and quaternionic vector bundles on a real algebraic curve. The basic relationship is established with unitary representations of an extension Z/2 by the fundamental group. By comparison with the space of…
In the first part of this paper, we propose a uniform interpretation of characteristic classes as obstructions to the reduction of the structure group and to the existence of an equivariant extension of a certain homomorphism defined a…
We define even dimensional quantum spheres Sigma_q^2n that generalize to higher dimension the standard quantum two-sphere of Podle's and the four-sphere Sigma_q^4 obtained in the quantization of the Hopf bundle. The construction relies on…
We investigate principal bundles over a root stack. In case of dimension one, we generalize the criterion of Weil and Atiyah for a principal bundle to have an algebraic connection.
Taking a groupoid C*-algebra approach to the study of the quantum complex projective spaces $\mathbb{P}^{n}\left( \mathcal{T}\right) $ constructed from the multipullback quantum spheres introduced by Hajac and collaborators, we analyze the…
A conic bundle or quadric bundle in characteristic 2 can have generic fiber which is nowhere smooth over the function field of the base variety. In that case, the generic fiber is called a quasilinear quadric. We solve some of the main…
Let $X$ be an irreducible smooth complex projective variety. Let $G$ be a linear algebraic group over $\mathbb{C}$. We define the notion of Lie algebroid valued connection on holomorphic principal $G$--bundles on $X$, and study their basic…
A stratified bundle is a fibered space in which strata are classical bundles and in which attachment of strata is controlled by a structure category of fibers. Well known results on fibre bundles are shown to be true for stratified bundles;…
A $\mathbb Q$-conic bundle germ is a proper morphism from a threefold with only terminal singularities to the germ $(Z \ni o)$ of a normal surface such that fibers are connected and the anti-canonical divisor is relatively ample. We obtain…
Let G be a simple linear algebraic group defined over the complex numbers. Fix a proper parabolic subgroup P of G and a nontrivial antidominant character \chi of P. We prove that a holomorphic principal G-bundle E over a connected complex…
For certain roots of unity, we consider the categories of weight modules over three quantum groups: small, un-restricted and unrolled. The first main theorem of this paper is to show that there is a modified trace on the projective modules…
We construct the quantum group $GL_q(2)$ as the semi-infinite cohomology of the tensor product of two braided vertex operator algebras based on the algebra $W_2$ with complementary central charges $c+\bar{c}=28$. The conformal field theory…
Let $\mathcal{A}_{q}$ be an arbitrary quantum cluster algebra with principal coefficients. We give the fundamental relations between the quantum cluster variables arising from one-step mutations from the initial cluster in…
A comodule algebra P over a Hopf algebra H with bijective antipode is called principal if the coaction of H is Galois and P is H-equivariantly projective (faithfully flat) over the coaction-invariant subalgebra B. We prove that principality…
We present two classes of examples of Hopf algebroids associated with noncommutative principal bundles. The first comes from deforming the principal bundle while leaving unchanged the structure Hopf algebra. The second is related to…
We study manifolds arising as spaces of sections of complex manifolds fibering over the projective line with normal bundle of each section isomorphic to several copies of O(k). Such manifolds provide a natural setting for certain integrable…