带巴拿赫代数系数的微分代数I：从C* 代数到谱曲线的K-理论
Differential algebras with Banach-algebra coefficients I: From C*-algebras to the K-theory of the spectral curve
摘要：
我们提出了一个算子系数版本的佐藤的无限维格拉斯曼流形，和tau函数。在这种情况下，交换微分算子的Burchnall-Chaundy环成为一个C* 代数，我们应用布朗-道格拉斯-菲尔莫尔理论，和谱环的拓扑不变量变得容易获得。我们构造KK类的谱曲线的环，并由事实上，所有的等谱Burchnall-Chaundy环组成的雅可比矩阵的曲线，我们比较（度-1）的K-同调曲线的雅可比矩阵。证明了紧算子的Burchnall-Chaundy C* 代数扩张是如何提供一族算子值τ-函数的。
英文摘要：
We present an operator-coefficient version of Sato's infinite-dimensional Grassmann manifold, and tau-function. In this context, the Burchnall-Chaundy ring of commuting differential operators becomes a C*-algebra, to which we apply the Brown-Douglas-Fillmore theory, and topological invariants of the spectral ring become readily available. We construct KK classes of the spectral curve of the ring and, motivated by the fact that all isospectral Burchnall-Chaundy rings make up the Jacobian of the curve, we compare the (degree-1) K-homology of the curve with that of its Jacobian. We show how the Burchnall-Chaundy C*-algebra extension of the compact operators provides a family of operator-valued tau-functions.
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