论文标题
在$ p $ - 代理及其双重
On $P$-algebras and their duals
论文作者
论文摘要
在摩尔和彼得森（Moore and Peterson）的基础上，由于玛格利斯（Margolis）而引起的$ p $ - 代数的概念是由斯特罗德（Steenrod）代数及其模块的案例激励的。我们进一步开发了该理论的各个方面，尤其集中在相干模块和有限的维数模块上。我们还讨论了$ p $ -Algebra及其综合的双Hopf代数。我们的目标之一是提供一系列技术，用于计算超过$ P $ - 代数及其双重的共同体学组，尤其是给出的结果。我们的大部分工作都隐含在Margolis和其他工作中，但我们不知道文献中的系统讨论。我们提供了一些示例，说明了拓扑应用，这些应用很容易从我们的结果中遵循。
The notion of $P$-algebra due to Margolis, building on work of Moore and Peterson, was motivated by the case of the Steenrod algebra at a prime and its modules. We develop aspects of this theory further, focusing especially on coherent modules and finite dimensional modules. We also discuss the dual Hopf algebra of $P$-algebra and its comodules. One of our aims is provide a collection of techniques for calculating cohomology groups over $P$-algebras and their duals, in particular giving vanishing results. Much of our work is implicit in that of Margolis and others but we are unaware of systematic discussions in the literature. We give some examples illustrating topological applications which follow easily from our results.
