A Hilbert C∗-module is a generalisation of a Hilbert space for which the inner product takes its values in a C∗-algebra instead of the complex numbers. We use the bracket product to construct some Hilbert C∗-modules over a group C∗-algebra which is generated by the group of translations associated with a wavelet. We shall investigate bracket products and their Fourier transform in the space of ...

Let ∆ be an arbitrary linear differential operator of the second order acting on functions on a (super)manifold M . In local coordinates ∆ = 1 2 S ∂b∂a +T a ∂a +R. The principal symbol of ∆ is the symmetric tensor field S, or the quadratic function S = 1 2 Spbpa on T ∗M . The principal symbol can be understood as a symmetric “bracket” on functions: {f, g} := ∆(fg) − (∆f) g − (−1)f (∆g) + ∆(1) f...

We show that for the Kauffman bracket skein module over the field of rational functions in variable A, the module of a connected sum of 3-manifolds is the tensor product of modules of the individual manifolds.

Considering the scattering of massless open strings attached to a D-string living in the B field background, we show that corresponding scattering upto the order of α ′2 is exactly given by the gauge theory on noncommutative background, which is characterized by the Moyal bracket. 1 Introduction After the novel work of Witten [1], it was realized that the low energy dynamics of open

Considering the scattering of massless open strings attached to a D2-brane living in the B field background, we show that corresponding scattering upto the order of α ′2 is exactly given by the gauge theory on noncommutative background, which is characterized by the Moyal bracket. 1 Introduction After the novel work of Witten [1], it was realized that the low energy dynamics of open

A covariant formalism for Moyal deformations of gauge theory and differential equations which determine Seiberg-Witten maps is presented. Replacing the ordinary product of functions by the noncommutative Moyal product, noncommutative versions of integrable models can be constructed. We explore how a Seiberg-Witten map acts in such a framework. As a specific example, we consider a noncommutative...

A Moyal deformation of a Clifford Cl(3, 1) Gauge Theory of (Conformal) Gravity is performed for canonical noncommutativity (constant Θ parameters). In the very special case when one imposes certain constraints on the fields, there are no first order contributions in the Θ parameters to the Moyal deformations of Clifford gauge theories of gravity. However, when one does not impose constraints on...

This paper discusses Penrose spin networks in relation to the bracket polynomial.

We study spanning properties of a family functions translated along simple model sets. characterize tight frame and dual generators for such irregular translates we apply the results to Gabor systems. use connection between sets almost periodic rely strongly on Poisson summations formula introduce so-called bracket product, which then plays crucial role in our approach. As corollary main obtain...