We define *-Hopf algebras Fun(SLq(N, ℂ; ε1,…, ε_N_)), Fun(Oq(N, ℂ; ε1,…, ε_N_)) and Fun(Spq(n, ℂ; ε1,…, ε2_n_)) as the real complexifications of *-Hopf algebras Fun(SUq(N, ℂ; ε1,…, ε_N_)), Fun(Oq(N, ℂ; ε1,…, ε_N_)) and Fun(Spq(N, ℂ; ε1,…, ε2_n_)) of [RTF] (for q > 0). Such construction can be done for each coquasitriangular (CQT) *-Hopf algebra A. The obtained object Aℂℝ is also a CQT *-Hopf algebra. We describe the theory of corepresentations of Aℂℝ in terms of such a theory for A.
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Piotr Podlés, Complex Quantum Groups and Their Real Representations. Publ. Res. Inst. Math. Sci. 28 (1992), no. 5, pp. 709–745DOI 10.2977/PRIMS/1195167933