论文标题
$ \ MATHCAL {A} \ MATHCAL {V} $在仿射空间上有限类型的模块
$\mathcal{A}\mathcal{V}$ modules of finite type on affine space
论文作者
论文摘要
我们研究了载体空间上向量字段的Lie代数$ \ Mathcal {V} $的兼容动作的模块类别，而多项式函数的代数$ \ Mathcal {A} $。我们表明，在$ \ Mathcal {a} $上有限生成的此类别中的模块是免费的。我们还表明，这对兼容的动作等同于对差分运算符代数的通勤行动，而矢量场的谎言代数在起源中消失了。这使我们能够构建对仪表模块等模块的明确实现。
We study the category of modules admitting compatible actions of the Lie algebra $\mathcal{V}$ of vector fields on an affine space and the algebra $\mathcal{A}$ of polynomial functions. We show that modules in this category which are finitely generated over $\mathcal{A}$, are free. We also show that this pair of compatible actions is equivalent to commuting actions of the algebra of differential operators and the Lie algebra of vector fields vanishing at the origin. This allows us to construct explicit realizations of such modules as gauge modules.
