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'Wick rotations': The noncommutative hyperboloids and other surfaces of rotations

Research output: Contribution to journalJournal article

Published

Journal publication date01/1999
JournalLetters in Mathematical Physics
Journal number2
Volume47
Number of pages13
Pages97-109
Original languageEnglish

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.