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 $\mathrm{DY}({\mathfrak{gl}}_{m|n})$ 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 $\mathrm{DY}({\mathfrak{gl}}_{m|n})$.

12 pages, minor changes and corrections

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Cited by in corpus (1)

• Quantum Berezinian for quantum affine superalgebra $U_q({\widehat{gl}}_{M|N})$