标题： 辛Hodge理论在李代数束上 显示英文标题

标题： Symplectic Hodge Theory on Lie Algebroids

摘要： 我们探讨了Brylinksi条件、强Lefschetz条件以及Symplectic Geometry中由Brylinksi、Mathieu、Yan和Guillemin最初研究的$d\delta$-引理的自然类似条件。这三种条件的等价性被重新建立为一个纯粹的代数陈述，同时结合了Tseng、Yau和Ho建立的$d\delta$-引理的基本概念。然后我们将这种代数理论应用于所需的几何设置，以证明这些类似条件成立，并最后提供几个例子类别。 显示英文摘要

摘要： We explore the natural analogues of the Brylinksi condition, Strong Lefschetz condition, and $d\delta$-lemma in Symplectic Geometry originally explored by Brylinksi, Mathieu, Yan, and Guillemin in the Symplectic Lie Algebroid case. The equivalence of the three conditions is re-established as a purely algebraic statement along with a primitive notion of the $d\delta$-lemma established by Tseng, Yau, and Ho. We then apply this algebraic theory to the desired geometric setting to show that these analogues hold, and finally provide a few classes of examples.