Drinfeld super Yangian of the exceptional Lie superalgebra $D(2,1;\lambda)$

Abstract

In this paper, we establish the first rigorous framework for the Drinfeld super Yangian associated with an exceptional Lie superalgebra, which lacks a classical Lie algebraic counterpart. Specifically, we systematically investigate the Drinfeld presentation and structural properties of the super Yangian associated with the exceptional Lie superalgebra $D(2,1;\lambda)$. First, we introduce a Drinfeld presentation for the super Yangian associated with the exceptional Lie superalgebra $D(2,1;\lambda)$, explicitly constructing its current generators and defining relations. A key innovation is the construction of a Poincar\'e-Birkhoff-Witt (PBW) basis using degeneration techniques from the corresponding quantum loop superalgebra. Furthermore, we demonstrate that the super Yangian possesses a Hopf superalgebra structure, explicitly providing the coproduct, counit, and antipode.