加权微分泊松代数的泛包络代数
Universal enveloping algebras of weighted differential Poisson algebras
AI总结：
本文推广微分泊松代数，引入λ-微分泊松代数及其修正版本，证明其张量积封闭性，并构造泛包络代数，获得三个同构关系。
摘要：
λ-微分算子和修正λ-微分算子是经典微分算子的推广。本文引入了λ-微分泊松（简称λ-DP）代数和修正λ-微分泊松（简称λ-mDP）代数作为微分泊松代数的推广。证明了λ-DP代数在张量积下封闭，并在λ-DP代数的上同调代数上给出了λ-DP代数结构。这些结论也应用于λ-mDP代数及其模。最后，通过构造一个P-三元组，推广了λ-DP代数的泛包络代数。得到了对极代数、张量代数与λ-DP代数的泛包络代数之间的三个同构。
英文摘要：
The $λ$-differential operators and modified $λ$-differential operators are generalizations of classical differential operators. This paper introduces the notions of $λ$-differential Poisson ($λ$-DP for short) algebras and modified $λ$-differential Poisson ($λ$-mDP for short) algebras as generalizations of differential Poisson algebras. The $λ$-DP algebra is proved to be closed under tensor product, and a $λ$-DP algebra structure is provided on the cohomology algebra of the $λ$-DP algebra. These conclusions are also applied to $λ$-mDP algebras and their modules. Finally, the universal enveloping algebras of $λ$-DP algebras are generalized by constructing a $\mathcal{P}$-triple. Three isomorphisms among opposite algebras, tensor algebras and the universal enveloping algebras of $λ$-DP algebras are obtained.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
