Three-dimensional differential calculus on quantum spheres SZu~, # E ] -1, 1[\{0}, c e [0, c~], is introduced and Investigated. Spectra of generalized Laplacians are found. These operators are expressed by generalized directional derivatives. Classical limits of these objects are obtained and a simp
Differential calculus on quantum Euclidean spheres
β Scribed by M. Welk
- Book ID
- 110426353
- Publisher
- Springer
- Year
- 2000
- Tongue
- English
- Weight
- 322 KB
- Volume
- 50
- Category
- Article
- ISSN
- 0011-4626
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π SIMILAR VOLUMES
We show that the relations which define the algebras of the quantum Euclidean planes R N q can be expressed in terms of projections provided that the unique central element, the radial distance from the origin, is fixed. The resulting reduced algebras without center are the quantum Euclidean spheres
The quantum Euclidean spheres, S N-1 q , are (noncommutative) homogeneous spaces of quantum orthogonal groups, SO q (N). The \* -algebra A(S N-1 q ) of polynomial functions on each of these is given by generators and relations which can be expressed in terms of a self-adjoint, unipotent matrix. We e