Quotient rings of ??₂∧??₂
Quotient rings of ??₂∧??₂
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??????????????的商环
DOI：
10.1090/tran/8512
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发表时间：
2021
影响因子：
1.3
通讯作者：
Zeng, Mingcong
中科院分区：
文献类型：
--
作者：
Beaudry, Agnès;Hill, Michael;Lawson, Tyler;Shi, XiaoLin Danny;Zeng, Mingcong
本文研究了交换环谱上的模，其系数群是对偶Steenrod代数的商，由Milnor生成子的集合构成。我们证明了这些商中很少有承认代数结构的商，但那些承认代数结构的商可以简单地构造：在结合代数的范畴中自由地杀死一个生成子，杀死更高的生成子。利用对偶Steenrod代数中共轭运算的新信息，我们还考虑了Milnor生成族及其共轭的商。这使我们可以得到一组共轭代数，它们的系数环是有限维的，并表现出意想不到的对偶特征。然后我们用这些代数给出了环谱上若干模的同伦群的详细计算。参考文献
We study modules over the commutative ring spectrum, whose coefficient groups are quotients of the dual Steenrod algebra by collections of the Milnor generators. We show that very few of these quotients admit algebra structures, but those that do can be constructed simply: killing a generatorin the category of associative algebras freely kills the higher generators. Using new information about the conjugation operation in the dual Steenrod algebra, we also consider quotients by families of Milnor generators and their conjugates. This allows us to produce a family of associative-algebras whose coefficient rings are finite-dimensional and exhibit unexpected duality features. We then use these algebras to give detailed computations of the homotopy groups of several modules over this ring spectrum. References