On spectra realizing exterior parts of the steenrod algebra
On spectra realizing exterior parts of the steenrod algebra
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DOI：
10.1016/0040-9383(71)90017-6
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发表时间：
1971-03
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影响因子：
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通讯作者：
H. Toda
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文献类型：
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作者：
H. Toda
设p为素数，d为Steenrod代数mod p.分别用θ和Q表示由约化幂运算pi，i> 0（Pi= Sq”，如果p = 2）和Lilnor元素Qi，i 2 0（Qi = A，Qi+ I=[P '，Qi]）生成的Hopf子代数.然后，对于奇数p，乘法给出同构Q@9 g &。si'和θ'（p> 2）分别由Eilenberg-MacLane谱和Brown-Peterson谱的上同调实现，但是Q在多大程度上可以由某些谱的上同调实现为d-模还不清楚。这里我们知道Q的&-模结构由自然映射诱导的双射Q-+ d//9给出。
LET p be a prime and d be the Steenrod, algebra mod p. Denote by 9 and Q the Hopf subalgebras of & generated by the reduced power operations pi, i> 0,(Pi= Sq” ifp= 2), and by; Llilnor’s elements Qi, i 2 0 (Q,= A, Qi+ I=[P’, Q,]), respectively. Then for odd p, the multiplication gives an isomorphism Q@ 9 g &. si’and 9’(p> 2) are realized by the cohomologies of an Eilenberg-MacLane spectrum and Brown-Peterson’s spectrum, respectively; it is, however, not known that up to what degree can Q be realized as d-module by the cohomology of some spectrum? Here we understand that the &-module structure of Q is given by the bijection Q-+ d//9 induced by the natural map.