$\mathfrak{R}$-matrix for quantum superalgebra $\mathfrak{sl}(2|1)$ at roots of unity and its application to centralizer algebras

Abstract: We consider fundamental facts from the theory of Hopf superalgebras. We use them to construct the quantum double of the quantum superalgebra $sl(2|1)$ at roots of unity. Thus we obtain a multiplicative formula for universal $R$-matrix. Next we construct an $R$-matrix to investigate parametrized family of centralizer algebras. We give multiplication laws in particular case and describe a structure of such algebras in the general case.