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

Lucia Bagnoli, Slaven Kožić

In this note, we generalize the notion of quantum Berezinian to the double Yangian $\mathrm{DY}({\mathfrak{gl}}_{m|n})$ of the Lie superalgebra ${\mathfrak{gl}}_{m|n}$. We show that its c…