标题： 特殊李超代数 $D(2,1;\lambda)$ 的 Drinfeld 超 Yangian 显示英文标题

标题： Drinfeld super Yangian of the exceptional Lie superalgebra $D(2,1;λ)$

摘要： 本文建立了与例外李超代数相关的德拉infeld超杨振宁的第一个严格框架，这缺乏经典的李代数对应物。 具体来说，我们系统地研究了与例外李超代数$D(2,1;\lambda)$相关的超杨振宁的德拉infeld表示和结构特性。 首先，我们介绍了与例外李超代数$D(2,1;\lambda)$相关的超杨振宁的德拉infeld表示，明确构造了它的电流生成元和定义关系。 一个关键的创新是利用相应量子环超代数的退化技术构建了一个庞加莱-伯克霍夫-维特定理（PBW）基。 此外，我们证明了超杨振宁具有Hopf超代数结构，明确给出了其余配对、余单位和反极性。 显示英文摘要

摘要： 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.