4 papers
The Deformation Quantization of $\Real^n$ via the specifiaction of the commutators
Jonathan Gratus
In a deformation quantization of $\Real^n$, the Jacobi identity is automatically satisfied. This article poses the contrary question: Given a set of commutators which satisfies the…
Algebraic Noncommutative Geometry
Jonathan Gratus
A noncommutative algebra , called an algebraic noncommutative geometry, is defined, with a parameter in the centre. When is set to zero, the commutative algebra of…
"Wick Rotations": The Noncommutative Hyperboloids, and other surfaces of rotations
Jonathan Gratus
A ``Wick rotation'' is applied to the noncommutative sphere to produce a noncommutative version of the hyperboloids. A harmonic basis of the associated algebra is given. It is note…
An Introduction to the Noncommutative Sphere and some Extensions
Jonathan Gratus
This is a copy of the talk given at the conference ``Methods in Field Theory'' at Stara Lesna, The Slovak Republic, Sepemeber 22-26, 1997. An introduction to the noncommutative sph…