Mathematics – Quantum Algebra
Scientific paper
1998-01-08
Mathematics
Quantum Algebra
Latex, 12 pages, 0 figures, submitted to Lett. Math. Phys
Scientific paper
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 noted that, for the one sheeted hyperboloid, the vector space for the noncommutative algebra can be completed to a Hilbert space, where multiplication is not continuous. A method of constructing noncommutative analogues of surfaces of rotation, examples of which include the paraboloid and the $q$-deformed sphere, is given. Also given are mappings between noncommutative surfaces, stereographic projections to the complex plane and unitary representations. A relationship with one dimensional crystals is highlighted.
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