ISSN:
1572-9168
Keywords:
16W30
;
17B37
;
22E99
;
quantum groups
;
quantum homogeneous spaces
;
coaction
;
dual Hopf algebras
;
two-sided coideals
;
infinitesimal invariance
;
quantum SU(2)
;
sl(2) quantized universal enveloping algebra
;
quantum 2-spheres
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract For a quantum groupG the notion of quantum homogeneousG-space is defined. Two methods to construct such spaces are discussed. The first one makes use of quantum subgroups, the second more general one is based upon the notion of infinitesimal invariance with respect to certain two-sided coideals in the Hopf algebra dual to the Hopf algebra ofG. These methods are applied to the quantum group SU(2). As two-sided coideals we take the subspaces spanned by twisted primitive elements in the sl(2) quantized universal enveloping algebra. A one-parameter series of mutually non-isomorphic quantum 2-spheres is obtained, together with the spectral decomposition of the corresponding right regular representation of quantum SU(2). The link with the quantum spheres defined by Podleś is established.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01278478
