arXiv subjects
Publications and source records attributed to Fengchang Li.
We give the explicit formula of the universal $R$-matrix of a double parameter (or two-parameter, or multi-parameter) quantum affine algebra of type ${\mathrm{A}}_1^{(1)}$. For $N$ with $q_{00}q_{01}$ being a primitive $N$-th root of unity, we introduce its $2N$-dimensional representation and explicitly calculate the $R$-matrix associated with it via the universal $R$-matrix.
We describe the subracks of the conjugacy classes of $\mathrm{PSL}(2,q)$ based on Dickson's theorem on subgroups of $\mathrm{PSL}(2,q)$. All minimal non-abelian subracks of $\mathrm{PSL}(2,q)$ are determined. Further, we provide a general result on the relationship of associated groups of conjugacy classes in perfect groups to the Schur multiplier of the group. This allows us to conclude explicit descriptions of the associated groups and the second homology of the conjugacy classes of $\mathrm{PSL}(2,q)$ for $q>3$.
We research $U_{v}(A(0,2)^{(4)})^{+}$ defined by quantum Serre relations, when $v$ is not a root of unity. We prove that $U_{v}(A(0,2)^{(4)})^{+}$ is isomorphic to a Nichols algebra. In other words, it is equivalent to define $U_{v}(A(0,2)^{(4)})^{+}$ by quantum Serre relations and by the radical of the bilinear form. We determine all the root multiplicities and give a PBW basis of $U_{v}(A(0,2)^{(4)})^{+}$.