ABSTRACT

We introduce a new operator – a modified λ-differential operator – from a usual differential operator. We construct the free (modified) λ-differential $(\mathbf{k},\mathrm{\partial })$-algebra on a (modified) differential $(\mathbf{k},\mathrm{\partial })$-module, and apply it to erect the universal enveloping (modified) differential algebra of a (modified) λ-differential Lie $(\mathbf{k},\mathrm{\partial })$-algebra. The corresponding Poincaré-Birchoff-Witt theorems are obtained. The Wronskian envelope of a modified λ-differential Lie $(\mathbf{k}\mathbf{,}\mathbf{-}\lambda {\mathrm{i}\mathrm{d}}_{\mathbf{k}})$-algebra is also constructed.

中文翻译：

---

（修正的）λ-微分李代数的通用包络

摘要

我们从通常的微分算子中引入了一个新的算子——一个改进的λ -微分算子。我们构造了自由（修改的）λ-微分$(\mathbf{ķ},\mathrm{\partial })$-（修改的）微分上的代数$(\mathbf{ķ},\mathrm{\partial })$-模，并应用它来建立一个（修正）λ-微分李的全包络（修正）微分代数$(\mathbf{ķ},\mathrm{\partial })$-代数。得到相应的 Poincaré-Birchoff-Witt 定理。修正的λ -微分 Lie的 Wronskian 包络$(\mathbf{ķ}\mathbf{,}\mathbf{-}\lambda {\mathrm{一世}\mathrm{d}}_{\mathbf{ķ}})$-代数也被构造。