复$K$ -理论合作代数的一个新基
A new basis for the complex $K$-theory cooperations algebra
摘要：
Adams、Harris和Switzer的一个经典定理指出，复$K$ -理论合作的第0阶，$KU_0ku$同构于数值多项式空间。数值多项式的空间具有由二项式系数多项式提供的基，其给出$KU_0ku$的基。本文利用Adams分裂构造了$KU_0ku_{(p)}$的一个新的$p$ -局部基.这个基础是通过使用众所周知的公式Hazewinkel生成器。对于$p=2$，我们表明，这个新的基础与经典的基础模更高的亚当斯过滤。
英文摘要：
A classical theorem of Adams, Harris, and Switzer states that the 0th grading of complex $K$-theory cooperations, $KU_0ku$ is isomorphic to the space of numerical polynomials. The space of numerical polynomials has a basis provided by the binomial coefficient polynomials, which gives a basis of $KU_0ku$. In this paper, we produce a new $p$-local basis for $KU_0ku_{(p)}$ using the Adams splitting. This basis is established by using well known formulas for the Hazewinkel generators. For $p=2$, we show that this new basis coincides with the classical basis modulo higher Adams filtration.
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