相关论文: The K-Theory of Heegaard-Type Quantum 3-Spheres
From the homotopy groups of three distinct octahedral spherical 3-manifolds we construct the isomorphic groups H of deck transformations acting on the 3-sphere. The H-invariant polynomials on the 3-sphere constructed by representation…
A large class of noncommutative spherical manifolds was obtained recently from cohomology considerations. A one-parameter family of twisted 3-spheres was discovered by Connes and Landi, and later generalized to a three-parameter family by…
This is the third of a series of papers on a new equivariant cohomology that takes values in a vertex algebra, and contains and generalizes the classical equivariant cohomology of a manifold with a Lie group action a la H. Cartan. In this…
Given a genus-g Heegaard splitting of a 3-sphere, the genus-g Goeritz group is defined to be the group of the isotopy classes of orientation preserving homeomorphism of the 3-sphere that preserve the splitting. In this paper, we determine…
We show that the Hausdorffized algebraic K-theory of a C*-algebra decomposes naturally as a direct sum of the Hausdorffized unitary algebraic K-theory and the space of continuous affine functions on the trace simplex. Under mild regularity…
For a genus $g$ Heegaard splitting of the $3$-sphere, the Goeritz group is defined to be the group of isotopy classes of diffeomorphisms of the $3$-sphere that preserve the splitting setwise. In this paper, we prove the following conjecture…
We introduce and study a new class of algebras, which we name \textit{quantum generalized Heisenberg algebras} and denote by $\mathcal{H}_q (f,g)$, related to generalized Heisenberg algebras, but allowing more parameters of freedom, so as…
We study deformation of algebras with coaction symmetry of reduced algebra of discrete groups, where the deformation parameter is given continuous family of group $2$-cocycles. When the group satisfies the Baum-Connes conjecture with…
Using the Baum-Connes conjecture with coefficients, we develop a K-theory formula for reduced C*-algebras of strongly $0$-$E$-unitary inverse semigroups, or equivalently, for certain reduced partial crossed products. In the case of…
A one parameter set of noncommutative complex algebras is given. These may be considered deformation quantisation algebras. The commutative limit of these algebras correspond to the algebra of polynomial functions over a manifold or…
We study the scalar quantum field theory on a generic noncommutative two-sphere as a special case of noncommutative curved space, which is described by the deformation quantization algebra obtained from symplectic reduction and parametrized…
It is shown that q-deformed quantum mechanics (q-deformed Heisenberg algebra) can be interpreted as quantum mechanics on Kaehler manifolds, or as a quantum theory with second (or first-) class constraints. (Saclay, T93/027).
The classification of the unitary irreducible representations of symmetry groups is a cornerstone of modern quantum physics, as it provides the fundamental building blocks for constructing the Hilbert spaces of theories admitting these…
For a given finite dimensional Hopf algebra $H$ we describe the set of all equivalence classes of cocycle deformations of $H$ as an affine variety, using methods of geometric invariant theory. We show how our results specialize to the…
The quantum field algebra of real scalar fields is shown to be an example of infinite dimensional quantum group. The underlying Hopf algebra is the symmetric algebra S(V) and the product is Wick's normal product. Two coquasitriangular…
The Turaev-Viro invariants are scalar topological invariants of compact, orientable 3-manifolds. We give a quantum algorithm for additively approximating Turaev-Viro invariants of a manifold presented by a Heegaard splitting. The algorithm…
This paper aims at developing a "local--global" approach for various types of finite dimensional algebras, especially those related to Hecke algebras. The eventual intention is to apply the methods and applications developed here to the…
The present paper starts with an introduction to quaternions and then defines the 3-dimmensional sphere as the set of quaternions of length one. The quaternion group induces on $\mathbb{S}^3$ a structure of noncommutative Lie group. This…
Gelfand - Na\u{i}mark theorem supplies a one to one correspondence between commutative $C^*$-algebras and locally compact Hausdorff spaces. So any noncommutative $C^*$-algebra can be regarded as a generalization of a topological space.…
We define the spherical Hecke algebra H for an almost split Kac-Moody group G over a local non-archimedean field. We use the hovel I associated to this situation, which is the analogue of the Bruhat-Tits building for a reductive group. The…