Real forms of quantum orthogonal groups, q-Lorentz groups in any dimension

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 \cite{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 analized.

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