AI 中文总结
本文发展交换泊松代数的扩张理论，定义其二阶上同调并建立该上同调群与一类特殊扩张等价类间的自然双射对应。
AI 中文摘要
本文发展交换泊松代数的扩张理论，具体定义了交换泊松代数$K$在阿贝尔泊松代数$H$系数下的二阶上同调，并建立该上同调群与一类特殊扩张的等价类集合之间的自然双射对应。
英文摘要
In this paper, we develop the extension theory of commutative Poisson algebras. Specifically, we define the second cohomology of a commutative Poisson algebra $K$ with coefficients in an abelian Poisson algebra $H$. We then establish a natural bijective correspondence between this cohomology group and the set of equivalence classes of a special type of extensions.
