Abstract
AbstractA list of known quantum spheres of dimension one, two and three is presented. M.S.C. : 81R60, 81R50, 20G42, 58B34, 58B32, 17B37. Key words and phrases : Noncommutative geometry, quantum spheres.Ref. SISSA 79/2001/FM 0. Introduction. Recently, examples of quantum spheres cropped in abundance in the literature. The goal ofthis note is to aid the book-keeping of these newly emerged species by systematically comparingtheir basic properties.As is customary in noncommutative geometry, these quantum spaces are described and stud-ied in terms of certain noncommutative algebras, generalizing the usual correspondence betweenspaces and function algebras. Here I am concerned mainly with ‘deformations’ of the ∗-algebra ofpolynomials on the sphere S n and their enveloping C ∗ -algebras. The ∗-algebras are usually givenin terms of generators and relations. Some of these relations can be regarded as deformationsof the commutation relations and some as deformations of the sphere relationP n+1j
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