Related papers: A Note on Spectral Triples on the Quantum Disk
We announce a result on quantum McKay correspondence for disc invariants of outer legs in toric Calabi-Yau 3-orbifolds, and illustrate our method in a special example $[\mathbb C^3 /\mathbb Z_5 (1, 1, 3)]$.
Significant developments made in quantum hardware and error correction recently have been driving quantum computing towards practical utility. However, gaps remain between abstract quantum algorithmic development and practical applications…
We construct spectral triples on all Podles quantum spheres. These noncommutative geometries are equivariant for a left action of $U_q(su(2))$ and are regular, even and of metric dimension 2. They are all isospectral to the undeformed round…
In this paper we will demonstrate that any compact quantum group can be used as symmetry groups for quantum channels, which leads us to the concept of covariant channels. We, then, unearth the structure of the convex set of covariant…
An invariant of three-dimensional orientable manifolds is built on the base of a solution of pentagon equation expressed in terms of metric characteristics of Euclidean tetrahedra.
We obtain an explicit characterization of linear maps, in particular, quantum channels, which are covariant with respect to an irreducible representation ($U$) of a finite group ($G$), whenever $U \otimes U^c$ is simply reducible (with…
We determine the quantum cohomology of the moduli space of odd degree rank two stable vector bundles over a Riemann surface $\Sigma$ of any genus. This work together with dg-ga/9710029 prove that this quantum cohomology is isomorphic to the…
We refine the reconstruction theorem for almost-commutative spectral triples to a result for real almost-commutative spectral triples, clarifying, in the process, both concrete and abstract definitions of real commutative and…
Fock-Goncharov's moduli spaces $\mathscr{X}_{{\rm PGL}_3,\frak{S}}$ of framed ${\rm PGL}_3$-local systems on punctured surfaces $\frak{S}$ provide prominent examples of cluster $\mathscr{X}$-varieties and higher Teichm\"uller spaces. In a…
We construct a 3^+ summable spectral triple (A(SU_q(2)),H,D) over the quantum group SU_q(2) which is equivariant with respect to a left and a right action of U_q(su(2)). The geometry is isospectral to the classical case since the spectrum…
Using the fact that the algebra M(3,C) of 3 x 3 complex matrices can be taken as a reduced quantum plane, we build a differential calculus Omega(S) on the quantum space S defined by the algebra C^\infty(M) \otimes M(3,C), where M is a…
A framework which combines ideas from Connes' noncommutative geometry, or spectral geometry, with recent ideas on generally covariant quantum field theory, is proposed in the present work. A certain type of spectral geometries modelling…
We describe a way to deform spectral triples with a 2-torus action and a real deformation parameter, motivated by deformation of manifolds after Connes-Landi. Such deformations are shown to have naturally isomorphic $K$-theoretic invariants…
Triple linking numbers were defined for 3-component oriented surface-links in 4-space using signed triple points on projections in 3-space. In this paper we give an algebraic formulation using intersections of homology classes (or cup…
We construct a spectral triple for the C$^*$-algebra of continuous functions on the space of $p$-adic integers by using a rooted tree obtained from coarse-grained approximation of the space, and the forward derivative on the tree.…
We study a three-dimensional differential calculus on the standard Podles quantum two-sphere S^2_q, coming from the Woronowicz 4D+ differential calculus on the quantum group SU_q(2). We use a frame bundle approach to give an explicit…
We study almost real spectral triples on quantum lens spaces, as orbit spaces of free actions of cyclic groups on the spectral geometry on the quantum group $SU_q(2)$. These spectral triples are given by weakening some of the conditions of…
A set of data supposed to give possible axioms for spacetimes with a sufficient number of isometries in spectral geometry is given. These data are shown to be sufficient to obtain 1+1 dimensional de Sitter spacetime. The data rely at the…
We construct spectral triples and, in particular, Dirac operators, for the algebra of continuous functions on certain compact metric spaces. The triples are countable sums of triples where each summand is based on a curve in the space.…
We construct the generalized version of covariant Z_3-graded differential calculus introduced by one of us (R.K.), and then extended to the case of arbitrary Z_N grading. Here our main purpose is to establish the recurrence formulae for the…