On rationalized H- and co-H-spaces with an appendix on decomposable H- and co-H-spaces
On rationalized H- and co-H-spaces with an appendix on decomposable H- and co-H-spaces
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关于有理化 H 和余 H 空间以及可分解 H 和余 H 空间的附录
DOI：
10.1007/bf01168347
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发表时间：
1985
影响因子：
0.6
通讯作者：
H. Scheerer
中科院分区：
文献类型：
--
作者：
H. Scheerer
设R是1/2,1/3∈R的有理数的子函数；设srn0表示r -局部n球，定义ΩRn:= srn_n为奇数，ΩRn:=ΩΣSRnfor n bbb_0为偶数。h空间。1-conn。co- h空间)是“可分解的”，如果它是同伦等价于空间的弱积ΩRn(参见。到r局部球体的楔形)。证明了函子[-，E]在有限复形上由Hopf代数M*（E；R）确定；其中M*为H.J. Baues的不稳定上同伦函子。如果C在R上是协群可分解的，则函子[C，-]是在1-conn上确定的。用π*（ΩC）作为m -李代数范畴中的一个余群来证明r -局部空间。对于R = Φ，函子[-，E]也由李代数π*(E)和[C，-]由与C的乘法相关的Berstein协代数决定。
Let R be a subring of the rationals with 1/2, 1/3∈R; let SRndenote the R-local n-sphere and define ΩRn:=SRnfor n odd, ΩRn:=ΩΣSRnfor n>0 even. An H-space (resp. a 1-conn. co-H-space) is “decomposable over R”, if it is homotopy equivalent to a weak product of spaces ΩRn(resp. to a wedge of R-local spheres). We prove that, if E is grouplike decomposable of finite type over R, the functor [-,E] is determined on finite dim. complexes by the Hopf algebra M*(E;R); here M*denotes the unstable cohomotopy functor of H.J. Baues. If C is cogrouplike decomposable over R, the functor [C,-] is determined on 1-conn. R-local spaces by π*(ΩC) as a cogroup in the category of M-Lie algebras. For R = Φ the functor [-,E] is also determined by the Lie algebra π*(E) and [C,-] by the Berstein coalgebra associated to the comultiplication of C.