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Real Forms of Quantum Orthogonal Groups, q-Lorentz Groups in any Dimension

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Abstract

We review known real forms of the quantum orthogonal groups SO q (N). New *-conjugations are then introduced and we contruct all real forms of quantum orthogonal groups. We thus give an RTT formulation of the *-conjugations on SO q (N) that is complementary to the U q (g) *-structure classification of Twietmeyer. In particular, we easily find and describe the real forms SO q (N-1,1) for any value of N. Quantum subspaces of the q-Minkowski space are analyzed.

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  1. Physics Division, Lawrence Berkeley National Laboratory, Theoretical Physics Group, 1 Cyclotron Road, Berkeley, California, 94720, U.S.A

    Paolo Aschieri

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  1. Paolo Aschieri
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Aschieri, P. Real Forms of Quantum Orthogonal Groups, q-Lorentz Groups in any Dimension. Letters in Mathematical Physics 49, 1–15 (1999). https://doi.org/10.1023/A:1007636508798

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