'Wick Rotations': The Noncommutative Hyperboloids and Other Surfaces of Rotations |
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Authors: | Gratus Jonathan |
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Institution: | (1) Department of Mathematics, Warsaw University, Banacha 2, 02-097 Warsaw, Poland |
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Abstract: | A 'Wick rotation' is applied to a noncommutative sphere to produce a noncommutative version of the hyperboloids. A harmonic basis of the associated algebra is given. 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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Keywords: | noncommutative geometry hyperboloids surfaces of rotations |
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