Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - 'Wick rotations': The noncommutative hyperboloids and other surfaces of rotations
AU - Gratus, Jonathan
PY - 1999/1
Y1 - 1999/1
N2 - 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.
AB - 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.
KW - hyperboloids
KW - surfaces of rotations
KW - QUANTUM RIEMANN SURFACES
KW - noncommutative geometry
U2 - 10.1023/A:1007557519016
DO - 10.1023/A:1007557519016
M3 - Journal article
VL - 47
SP - 97
EP - 109
JO - Letters in Mathematical Physics
JF - Letters in Mathematical Physics
SN - 0377-9017
IS - 2
ER -