标题： 非交换环上的形式群 显示英文标题

标题： Formal groups over non-commutative rings

摘要： 我们开发了通常形式群定律理论的一个扩展，其中基环不要求是交换的，而且形式变量也不必是中心的，也不必彼此交换。 我们证明，这种形式群定律是代数拓扑需求的自然类型，因为一个（可能非交换的）复定向环谱被规范地配备了这样一种形式群定律。 通用的形式群定律由Baker-Richter谱M{\xi }所携带，在这种非交换情境中，它起到类似于MU的作用。 正如Morava之前的研究所暗示的那样，Brouder、Frabetti和Krattenthaler所定义的“非交换直线的微分同胚”的Hopf代数B是这里所发展的理论的核心。 特别是，我们验证了Morava的猜想，即存在D(B)的表示通过M{\xi }中的上同调运算。 显示英文摘要

摘要： We develop an extension of the usual theory of formal group laws where the base ring is not required to be commutative and where the formal variables need neither be central nor have to commute with each other. We show that this is the natural kind of formal group law for the needs of algebraic topology in the sense that a (possibly non-commutative) complex oriented ring spectrum is canonically equipped with just such a formal group law. The universal formal group law is carried by the Baker-Richter spectrum M{\xi} which plays a role analogous to MU in this non-commutative context. As suggested by previous work of Morava the Hopf algebra B of "formal diffeomorphisms of the non-commutative line" of Brouder, Frabetti and Krattenthaler is central to the theory developed here. In particular, we verify Morava's conjecture that there is a representation of the Drinfeld quantum-double D(B) through cohomology operations in M{\xi}.