Structure of the Three-dimensional Quantum Euclidean Space

Details Structure of the Three-dimensional Quantum Euclidean Space Structure of the Three-dimensional Quantum Euclidean Space

2000-04-03

arxiv.org/abs/math/0004011v1

Eur.Phys.J.C16:169-180,2000

Mathematics

Quantum Algebra

22 pages, latex

Scientific paper

10.1007/s100520050013

As an example of a noncommutative space we discuss the quantum 3-dimensional Euclidean space $R^3_q$ together with its symmetry structure in great detail. The algebraic structure and the representation theory are clarified and discrete spectra for the coordinates are found. The q-deformed Legendre functions play a special role. A completeness relation is derived for these functions.

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