相关论文: Equivariant spectral triples on the quantum SU(2) …
Two examples of spectral triples with non-integer dimension spectrum are considered. These triples involve commutative C*-algebras. The first example has complex dimension spectrum and trivial differential algebra. The other is a parameter…
We compute the weighted Euler characteristic, equivariant with respect to the action of the symplectic group of degree six over the field of two elements, of the moduli space of principally polarized abelian threefolds together with a level…
We define a bigraded homology theory whose Euler characteristic is the quantum sl(3) link invariant.
Let $R$ be a ring with pseudo-involution, $\mathfrak L$ be an odd form parameter, $\mathrm U(2n,\,R,\,\mathfrak L)$ be an odd hyperbolic unitary group, $\mathrm{EU}(2n,\,R,\,\mathfrak L)$ be it elementary subgroup and…
We construct a new invariant of two-dimensional $\mathcal{N}{=}(0,1)$ supersymmetric quantum field theories (SQFTs), under a couple of assumptions on the general properties of such SQFTs motivated by considerations in heterotic string…
Definition of Dirac operators on the quantum group $SU_{q}(2)$ and the quantum sphere $S^{2}_{q \mu}$ are discussed. In both cases similar $SU_{q}(2)$-invariant form is obtained. It is connected with corresponding Laplace operators.
The present article investigates Sp(3) structures on 14-dimensional Riemannian manifolds, a continuation of the recent study of manifolds modeled on rank two symmetric spaces (here: SU(6)/Sp(3)). We derive topological criteria for the…
Recently we initiated the study of spherical T-duality for spacetimes that are principal SU(2)-bundles. In this paper, we extend spherical T-duality to spacetimes that are oriented non-principal SU(2)-bundles. There are several interesting…
N-fold supersymmetry is an extension of the ordinary supersymmetry in one-dimensional quantum mechanics. One of its major property is quasi-solvability, which means that energy eigenvalues can be obtained for a portion of the spectra. We…
A direct relationship between the (non-quantum) group SU(2) and the Kauffman bracket in the framework of Chern-Simons theory is explicitly shown.
Let $G\subset SO(4)$ denote a finite subgroup containing the Heisenberg group. In these notes we classify all these groups, we find the dimension of the spaces of $G$-invariant polynomials and we give equations for the generators whenever…
We study irreducible spherical unitary representations of the Drinfeld double of a $q$-deformation of a connected simply connected compact Lie group, which can be considered as a quantum analogue of the complexification of the Lie group. In…
We perform the momentum-space quantization of a spin-less particle moving on the $SU(2)$ group manifold, that is, the three-dimensional sphere $S^{3}$, by using a non-canonical method entirely based on symmetry grounds. To achieve this…
Results are obtained on extending flat vector bundles or equivalently general representations from the fundamental group of S, a connected subsurface of the connected boundary of a compact, connected, oriented 3-dimensional manifold, to the…
The discovery of the SU(3) symmetry was fundamental as to establishing an ordering principle in particle physics. We already studied how to couple the SU(3) symmetry to the gravitational field in four-dimensional curved Lorentzian…
We explain how a simple twisting of the notion of spectral triple allows to incorporate type III examples, such as those arising from the transverse geometry of codimension one foliations. Since the twisting of the commutators turns the…
An invariant for twisted K theory classes on a 3-manifold is introduced. The invariant is then applied to the twisted equivariant classes arising from the supersymmetric Wess-Zumino-Witten model based on the group SU(2). It is shown that…
We apply the Tannaka-Krein duality theory for quantum homogeneous spaces, developed in the first part of this series of papers, to the case of the quantum SU(2) groups. We obtain a classification of their quantum homogeneous spaces in terms…
Semiclassical quantization of the SU(3)-skyrmions is performed by means of the collective coordinate method. The quantization condition known for the SU(2)-solitons quantized with SU(3) collective coordinates is generalized for the SU(3)…
We construct globally-defined $SU(3)$ structures on smooth compact toric varieties (SCTV) in the class of $\mathbb{CP}^1$ bundles over $M$, where $M$ is an arbitrary SCTV of complex dimension two. The construction can be extended to the…