Non-commutative Euclidean structures in compact spaces
arXiv:hep-th/9907136 · doi:10.1088/0305-4470/34/12/306
Abstract
Based on results for real deformation parameter q we introduce a compact non- commutative structure covariant under the quantum group SOq(3) for q being a root of unity. To match the algebra of the q-deformed operators with necesarry conjugation properties it is helpful to define a module over the algebra genera- ted by the powers of q. In a representation where X is diagonal we show how P can be calculated. To manifest some typical properties an example of a one-di- mensional q-deformed Heisenberg algebra is also considered and compared with non-compact case.
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