On the Yangian Y $$(\mathfrak{g}\mathfrak{l}_{m|n} )$$ and its quantum Berezinian

Abstract

Jonathan Brundan and Alexander Kleshchev recently introduced a new family of presentations for the Yangian Y\((\mathfrak{g}\mathfrak{l}_n )\) of the general linear Lie algebra \(\mathfrak{g}\mathfrak{l}_n\). In this article, we extend some of their ideas to consider the Yangian Y\((\mathfrak{g}\mathfrak{l}_{m|n} )\) of the Lie superalgebra \(\mathfrak{g}\mathfrak{l}_{m|n}\). In particular, we give a new proof of the result by Nazarov that the quantum Berezinian is central.