We construct coordinate algebras of quantum orthogonal, special orthogonal and symplectic groups using M. Jimbo's solutions of the Yang-Baxter equation and determine their Peter-Weyl decompositions. To do this, we study some class of bialgebras and their group-like elements (quantum determinants). A new realization of the universal R-matrix is also given.
Cite this article
Takahiro Hayashi, Quantum Deformation of Classical Groups. Publ. Res. Inst. Math. Sci. 28 (1992), no. 1, pp. 57–81DOI 10.2977/PRIMS/1195168856