Related papers: Quantum Homogeneous Spaces as Quantum Quotient Spa…
We prove that the group of area-preserving diffeomorphisms of the 2-sphere admits a non-trivial homogeneous quasimorphism to the real numbers with the following property. Its value on any diffeomorphism supported in a sufficiently small…
A Q-homology plane is a normal complex algebraic surface having trivial rational homology. We obtain a structure theorem for Q-homology planes with smooth locus of non-general type. We show that if a Q-homology plane contains a non-quotient…
A method of constructing covariant differential calculi on a quantum homogeneous space is devised. The function algebra X of the quantum homogeneous space is assumed to be a left coideal of a coquasitriangular Hopf algebra H and to contain…
We present some new ideas on how to design analogue models of quantum fields living in curved spacetimes using ultra-cold atoms in optical lattices. We discuss various types of static and dynamical curved spacetimes achievable by simple…
A generalization of the quotient integral formula is presented and some of its properties are investigated. Also the relations between two function spaces related to the spacial homogeneous spaces are derived by using general quotient…
We describe geometrically the classical and quantum inhomogeneous groups $G_0=(SL(2, \BbbC)\triangleright \BbbC^2)$ and $G_1=(SL(2, \BbbC)\triangleright \BbbC^2)\triangleright \BbbC$ by studying explicitly their shape algebras as a spaces…
We develop the theory of arrangements of spheres. Consider a finite collection of codimension-$1$ subspheres in a positive-dimensional sphere. There are two posets associated with this collection: the poset of faces and the poset of…
The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…
We compute the Grothendieck group K_0 of non-commutative analogues of quantum projective space bundles. Our results specialize to give the Grothendieck groups of non-commutative analogues of projective spaces, and specialize to recover the…
We study various aspects on nontrivial logarithmic co-Higgs structure associated to unstable bundles on algebraic curves. We check several criteria for (non-)existence of nontrivial logarithmic co-Higgs structures and describe their…
We introduce quantum Boolean algebras which are the analogue of the Weyl algebras for Boolean affine spaces. We study quantum Boolean algebras from the logical and set theoretical viewpoints.
We study the behaviors of quantum groups under an edge contraction. We show that there exists an explicit embedding induced by an edge contraction operation. We further conjecture that this explicit embedding is a section of an explicit…
We consider some generalization of the theory of quantum states and demonstrate that the consideration of quantum states as sheaves can provide, in principle, more deep understanding of some well-known phenomena. The key ingredients of the…
We discuss examples of non-commutative spaces over non-archimedean fields. Those include non-commutative and quantum affinoid algebras, quantized K3 surfaces and quantized locally analytic p-adic groups.
We describe invariant principal and Cartan connections on homogeneous principal bundles and show how to calculate the curvature and the holonomy; in the case of an invariant Cartan connection we give a formula for the infinitesimal…
The quantum plane is the non-commutative polynomial algebra in variables $x$ and $y$ with $xy=qyx$. In this paper, we study the module variety of $n$-dimensional modules over the quantum plane, and provide an explicit description of its…
A general theory of quantum spinor structures on quantum spaces is presented, within the conceptual framework of the formalism of quantum principal bundles. Quantum analogs of all basic objects of the classical theory are constructed and…
We reconstruct a quantum group associated with any Lie algebra together with its representation theory from twisted homologies of generalized configuration spaces of disks. Along the way it brings new combinatorics to the theory, but our…
We present necessary and sufficient conditions for a group homomorphism between spaces of smooth sections of Lie group bundles to be a weighted composition operator. These results provide new insights into a wide range of problems related…
We propose a version of the non-relativistic quantum mechanics in which the pure states of a quantum system are described as sections of a Hilbert (generally infinitely-dimensional) fibre bundle over the space-time. There evolution is…