论文标题
k联合代数扭曲捆绑包的K理论
K-theory cohomology of associative algebra twisted bundles
论文作者
论文摘要
我们介绍和研究正式系列的联想代数$ a（\ mathfrak g）$ k $的理论，该系列具有无限lie-lie代数系数，该系数在任意紧凑的拓扑空间上。此类束的纤维由代数完成所有正式序列的空间的元素在复杂参数中，由具有规定的分析属性的有理函数提供。在本文中，我们介绍和研究twisted $ a（\ mathfrak g）$ - 捆绑$ a（\ mathfrak g），x）$ bundles $ buptles $ [\ mathcal {e}] $ a $ a（\ mathfrak g）$ a（\ mathfrak G）我们表明，对于任何扭曲的$ a（\ mathfrak g）$ - 捆绑$ \ mathcal {e} $，存在另一个捆绑包$ \ widetilde {\ mathcal {e}} $，使得$ k（a（\ mathfrak g），x）$的元素for $ \ \ themcal {e e} $均可代表。 $ [\ MATHCAL {e}]/[\ widetilde {\ Mathcal {e}}] $。组$ k（a（\ mathfrak g），x）$同构属性相对于张量产品，以及将$ x $减少到基础点的分裂属性。我们还确定了两个紧凑型空间$ x $和$ y $的因子$ x/y $的K组细胞的共同体。
We introduce and study a $K$-theory of twisted bundles for associative algebras $A(\mathfrak g)$ of formal series with an infinite-Lie algebra coefficients over arbitrary compact topological spaces. Fibers of such bundles are given by elements of algebraic completion of the space of all formal series in complex parameters, sections are provided by rational functions with prescribed analytic properties. In this paper we introduce and study K-groups $K(A(\mathfrak g), X)$ of twisted $A(\mathfrak g)$-bundles as equivalence classes $[\mathcal{E}]$ of $A(\mathfrak g)$-bundle $\mathcal{E}$. We show that for any twisted $A(\mathfrak g)$-bundle $\mathcal{E}$ there exist another bundle $\widetilde{\mathcal{E}}$ such that an element of $K(A(\mathfrak g), X)$ for $\mathcal{E}$ can be represented in the form $[\mathcal{E}]/[\widetilde{\mathcal{E}}]$. The group $K(A(\mathfrak g), X)$ homomorphism properties with respect to tensor product, and splitting properties with respect to reductions of $X$ into base points. We determine also cohomology of cells of K-groups for the factor $X/Y$ of two compact spaces $X$ and $Y$.
