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The classification of differential structures on quantum 2-spheres
Authors:Piotr Podleś
Affiliation:(1) RIMS, Kyoto University, 606 Kyoto, Japan;(2) Present address: Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw, Ho"zdot"a 74, PL 00-682 Warszawa, Poland
Abstract:
Exterior algebras of differential forms on quantum 2-spheresSqc2,qisin[–1, 1]/{0},cisin[0, infin] (c=0 forq=±1), are classified. In the definition of exterior algebras we assume the invariance w.r.t. the action of the quantumSU(2) group and ldquodimensionality conditionsrdquo (which imply that we deal with ldquotwo-dimensional manifoldsrdquo). The exterior algebras exist only forc=0 and are unique in that case. The corresponding generalized directional derivatives are provided.
Keywords:
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