A pairing theorem between multi-parameter bialgebra and its dual bialgebra
Let \(A\) be the FRT-bialgebra [see \textit{N. Yu. Reshetikhin, L. A. Takhtadzhyan}, and \textit{L. D. Faddeev}, Algebra Anal. 1, No. 1, 178-206 (1989; Zbl 0715.17015)] related to Hayashi's \(R\)-matrix depending on \(n-1\) non-zero constants. The authors construct a subalgebra \(H\) of the finite dual \(A^\circ\) generated by some skew-derivations. These generators satisfy some Serre-like relations. The main theorem says that the natural induced pairing between \(A\) and \(H\) is non-degenerate when the parameters are not roots of unity. In this case, a basis of \(H\) as vector space is also found. Proofs are mainly based on a deep knowledge of the action of \(H\) on \(A\). Remark: References 8 and 11 were not published when this paper appeared. The exact references are: 8. \textit{M. Guo, L. Jiang, E. X. Zhao}, A pairing theorem between a braided bialgebra and its dual bialgebra, J. Algebra 245, No. 2, 532-551 (2001; Zbl 1001.16023). 11. \textit{M. Guo, L. Jiang, E. Y. Zhao}, The construction of braid Hopf algebra, Commun. Algebra 30, No. 4, 1725-1750 (2002; Zbl 1007.16031).
scientific article; zbMATH DE number 1782132