论文标题
schur-sato理论用于准纤细环
Schur-Sato theory for quasi-elliptic rings
论文作者
论文摘要
准椭圆环的概念是由于试图对综合系统理论中发现的一系列接线环（例如通勤差分，差异，差异差异等）进行分类而出现的。它们包含在某些非交通性的“通用”环中，这是一种纯粹的代数类似物，对歧管上的伪差算子环，并接受（在某些轻度限制下）方便的代数几何描述（在某些轻度限制下）。该描述的一个重要代数部分是Schur -sato理论 - 对普通差分运算符的众所周知的理论的概括。该理论的某些部分是在一系列论文中开发的，主要用于维度二。 在本文中，我们以任意维度介绍了这一理论。我们将该理论应用于某些子空间（Schur对）的两个分类定理。它们对于上述准椭圆环的代数几何描述是必需的。 该理论是有效的，并且具有其他几种应用，其中是Abhyankar倒置公式的新证明。
The notion of quasi-elliptic rings appeared as a result of an attempt to classify a wide class of commutative rings of operators found in the theory of integrable systems, such as rings of commuting differential, difference, differential-difference, etc. operators. They are contained in a certain non-commutative "universal" ring - a purely algebraic analogue of the ring of pseudodifferential operators on a manifold, and admit (under certain mild restrictions) a convenient algebraic-geometric description. An important algebraic part of this description is the Schur-Sato theory - a generalisation of the well known theory for ordinary differential operators. Some parts of this theory were developed earlier in a series of papers, mostly for dimension two. In this paper we present this theory in arbitrary dimension. We apply this theory to prove two classification theorems of quasi-elliptic rings in terms of certain pairs of subspaces (Schur pairs). They are necessary for the algebraic-geometric description of quasi-elliptic rings mentioned above. The theory is effective and has several other applications, among them is a new proof of the Abhyankar inversion formula.
