QUANTUM HOMOGENEOUS SPACES, DUALITY AND QUANTUM 2-SPHERES

被引:54
作者
DIJKHUIZEN, MS
KOORNWINDER, TH
机构
[1] CWI,1090 GB AMSTERDAM,NETHERLANDS
[2] UNIV AMSTERDAM,FAC MATH & COMP SCI,1018 TV AMSTERDAM,NETHERLANDS
关键词
QUANTUM GROUPS; QUANTUM HOMOGENEOUS SPACES; COACTION; DUAL HOPF ALGEBRAS; 2-SIDED COIDEALS; INFINITESIMAL INVARIANCE; QUANTUM SU(2); SL(2) QUANTIZED UNIVERSAL ENVELOPING ALGEBRA; QUANTUM; 2-SPHERES;
D O I
10.1007/BF01278478
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
For a quantum group G the notion of quantum homogeneous G-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 of G. 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 Podles is established.
引用
收藏
页码:291 / 315
页数:25
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