A note on the quantum Berezinian for the double Yangian of the Lie superalgebra $\mathfrak{gl}_{m|n}$

Abstract

In this note, we generalize the notion of quantum Berezinian to the double Yangian ${\rm DY}(\mathfrak{gl}_{m|n})$ of the Lie superalgebra $\mathfrak{gl}_{m|n}$. We show that its coefficients form a family of algebraically independent topological generators of the center of ${\rm DY}(\mathfrak{gl}_{m|n})$.