An algebraic introduction to the Steenrod algebra
An algebraic introduction to the Steenrod algebra
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Steenrod 代数的代数介绍
DOI：
10.2140/gtm.2007.11.327
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
Larry Smith
中科院分区：
文献类型：
--
作者：
Larry Smith
这些笔记的目的是提供一个介绍Steenrod代数在代数的方式避免任何使用上同调运算。Steenrod代数是函子的自同态代数的一个子代数。所讨论的函子将伽罗瓦域上的向量空间赋予该向量空间上的多项式函数的代数：如果基域是素域，则该函子的自同态的子代数被证明是Steenrod代数，由Frobenius映射的变体的齐次分量生成。
The purpose of these notes is to provide an introduction to the Steenrod algebra in an algebraic manner avoiding any use of cohomology operations. The Steenrod algebra is presented as a subalgebra of the algebra of endomorphisms of a functor. The functor in question assigns to a vector space over a Galois field the algebra of polynomial functions on that vector space: the subalgebra of the endomorphisms of this functor that turns out to be the Steenrod algebra if the ground field is the prime field, is generated by the homogeneous components of a variant of the Frobenius map.