The Picard Group of Equivariant Stable Homotopy Theory
The Picard Group of Equivariant Stable Homotopy Theory
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等变稳定同伦理论的Picard群
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
J. May
中科院分区：
文献类型：
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作者：
H. Fausk;L. Lewis;J. May
设G是紧李群。将g谱稳定同伦范畴中可逆对象的Picard群（HoG S）用g的一类合适的同伦表示来描述，并结合tom Dieck和Petrie的结果，证明了g谱稳定同伦范畴中可逆对象的Picard群（HoG S），基于任意稳定同伦范畴C的单位对象的自同态环的Picard群在C的Picard群中的嵌入，我们推导出了一个精确序列，该序列给出了g的Burnside环的Picard群的本质代数描述。
Abstract Let G be a compact Lie group. We describe the Picard group Pic(HoG S ) of invertible objects in the stable homotopy category of G-spectra in terms of a suitable class of homotopy representations of G. Combining this with results of tom Dieck and Petrie, which we reprove, we deduce an exact sequence that gives an essentially algebraic description of Pic(HoG S ) in terms of the Picard group of the Burnside ring of G. The deduction is based on an embedding of the Picard group of the endomorphism ring of the unit object of any stable homotopy category C in the Picard group of C .