Let A be the C∗-algebra associated with SUq(2), let π be the representation by left multiplication on the L2 space of the Haar state and let D be the equivariant Dirac operator for this representation constructed by the authors earlier. We prove in this article that there is no operator other than the scalars in the commutant π(A)′ that has bounded commutator with D. This implies that the equiv...

Let A be the C-algebra associated with SUq(2), π be the representation by left multiplication on the L2 space of the Haar state and let D be the equivariant Dirac operator for this representation constructed by the authors earlier. We prove in this article that there is no operator other than the scalars in the commutant π(A) that has bounded commutator with D. This implies that the equivariant...

We introduce the notion of a semi-Riemannian spectral triple which generalizes the notion of spectral triple and allows for a treatment of semiRiemannian manifolds within a noncommutative setting. It turns out that the relevant spaces in noncommutative semi-Riemannian geometry are not Hilbert spaces any more but Krein spaces, and Dirac operators are Kreinselfadjoint. We show that the noncommuta...

We study the canonical quantization of the theory given by Chamseddine-Connes spectral action on a particular finite spectral triple with algebra M2(C) ⊕ C. We define a quantization of the natural distance associated with this noncommutative space and show that the quantum distance operator has a discrete spectrum. We also show that it would be the same for any other geometric quantity. Finally...

We study the “quantized calculus” corresponding to the algebraic ideas related to “twisted cyclic cohomology” introduced in [12]. With very similar definitions and techniques as those used in [9], we define and study “twisted entire cyclic cohomology” and the “twisted Chern character” associated with an appropriate operator theoretic data called “twisted spectral data”, which consists of a spec...

Semi-empirical computer modelling is used to investigate spectral matching in tandem and triple-junction thin film silicon solar cells. In amorphous/microcrystalline silicon (a-Si:H/μc-Si:H) tandem cells, current mis-match is offset by an increase in fill-factor, resulting in a broad peak in efficiency versus average photon energy. For a-Si:H/a-Si:H tandem cells, photo-generated currents in bot...

The recognition and the calculation of all branches of solutions of the nonlinear boundary value problems is difficult obviously. The complexity of this issue goes back to the being nonlinearity of the problem. Regarding this matter, this paper considers steady state reactive transport model which does not have exact closed-form solution and discovers existence of dual or triple solutions in so...

In this paper, we have illustrated the construction of a real structure on fuzzy sphere S*2 in its spin-1/2 representation. Considering SU(2) covariant Dirac and chirality operator given by U. C. Watamura [Commun. Math. Phys. 183, 365–382 (1997) Commun. 212, 395–413 (2000)], shown that is consistent with other spectral data for KO dimension-4 fulfilling zero order condition, where find it neces...

Given a unital and commutative algebra A associated to a spectral triple, we show how a differentiable structure is constructed on the spectrum of such an algebra whenever the spectral triple satisfies eight so-called “axioms”, in such a way that A ∼= C∞(M). This construction is the celebrated “reconstruction theorem” of Alain Connes [14], [21]. We discuss two spin manifolds, the circle and the...