# Complex Quantum Groups and Their Real Representations

### Piotr Podlés

Warsaw University, Warszawa, Poland

## Abstract

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.

## Cite this article

Piotr Podlés, Complex Quantum Groups and Their Real Representations. Publ. Res. Inst. Math. Sci. 28 (1992), no. 5, pp. 709–745

DOI 10.2977/PRIMS/1195167933