Related papers: A Cousin Complex for the Quantum Projective Space

In this paper we use the notion of Grothendieck topology to present a unified way to approach representability in supergeometry, which applies to both the differential and algebraic settings.

We generalize the asymptotic faithfulness of the skein quantum $SU(2)$ representations of mapping class groups of orientable closed surfaces to skein $SU(3)$. Skein quantum representations of mapping class groups are different from the…

Over the quantum weighted 1-dimensional complex projective spaces, called quantum teardrops, the quantum line bundles associated with the quantum principal U(1)-bundles introduced and studied by Brzezinski and Fairfax are explicitly…

The cusp was recently shown to admit the structure of a quantum homogeneous space, that is, its coordinate ring $B$ can be embedded as a right coideal subalgebra into a Hopf algebra $A$ such that $A$ is faithfully flat as a $B$-module. In…

For curved projective manifolds we introduce a notion of a normal tractor frame field, based around any point. This leads to canonical systems of (redundant) coordinates that generalise the usual homogeneous coordinates on projective space.…

Let $\mathfrak g$ be a complex simple Lie algebra and let $U_{\zeta}({\mathfrak g})$ be the corresponding Lusztig ${\mathbb Z}[q,q^{-1}]$-form of the quantized enveloping algebra specialized to an $\ell$th root of unity. Moreover, let…

We compute the equivariant cohomology of complex projective spaces associated to finite-dimensional representations of $C_2$, using ordinary cohomology graded on representations of the fundamental groupoid, with coefficients in the Burnside…

In this paper we present a new procedure to obtain unitary and irreducible representations of Lie groups starting from the cotangent bundle of the group (the cotangent group). We discuss some applications of the construction in…

In this paper, we study the structure of the quantum cohomology ring of a projective hypersurface with non-positive 1st Chern class. We prove a theorem which suggests that the mirror transformation of the quantum cohomology of a projective…

Motivated by the study of the interrelation between functorial and algebraic quantum field theory, we point out that on any locally trivial bundle of compact groups, representations up to homotopy are enough to separate points by means of…

We present a new construction for Poisson transforms between vector bundle valued differential forms on homogeneous parabolic geometries and the corresponding Riemannian symmetric space, which can be described in terms of finite dimensional…

An alternative to the representation of complex relativity by self-dual complex 2-forms on the spacetime manifold is presented by assuming that that the bundle of real 2-forms is given an almost-complex structure. From this, one can define…

The quantum group version of the Bernstein-Gelfand-Gelfand resolution is used to construct a double complex of U_q(g)-modules with exact rows and columns. The locally finite dual of its total complex is identified with the de Rham complex…

We discuss various notions generalizing the concept of a homogeneous space to the setting of locally compact quantum groups. On the von Neumann algebra level we find an interesting duality for such objects. A definition of a quantum…

We consider quantum group theory on the Hilbert space level. We find all unitary representations of three braided quantum groups related to the quantum ``ax+b'' group. First we introduce an auxiliary braided quantum group, which is…

In this note we propose a construction of the Hopf algebra of a complex analog of devided powers of the Weyl generators of a semisimple simply-laced quantum group. Here we consider the generators as positive, self-adjoint operators. In…

Quantum homogeneous supervector bundles arising from the quantum general linear supergoup are studied. The space of holomorphic sections is promoted to a left exact covariant functor from a category of modules over a quantum parabolic…

Representations of small quantum groups $u_q({\mathfrak{g}})$ at a root of unity and their extensions provide interesting tensor categories, that appear in different areas of algebra and mathematical physics. There is an ansatz by Lusztig…

This is the first of a series of two papers devoted to the partition function realization of Wilson surfaces in strict higher gauge theory. A higher version of the Kirillov-Kostant-Souriau theory of coadjoint orbits is presented based on…

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…