Structure of the Three-dimensional Quantum Euclidean Space
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hep-thmath-phmath.MP
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spacestructureeuclideanfunctionsquantumalgebraicclarifiedcompleteness
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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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