The Picard group of equivariant stable homotopy theory. (English) Zbl 1009.55006
For a compact Lie group \(G\), the isomorphism classes of invertible \(G\)-spectra form a group, \(\text{Pic} (HoG {\mathcal S})\), under the smash product. This paper shows that there is an exact sequence \(0\to\text{Pic} (A(G)) \to\text{Pic}(HoG {\mathcal S})\to C(G)\), which gives an essentially algebraic description of Picard group \(\text{Pic} (HoG{\mathcal S})\) in terms of the Picard group of the Burnside ring of \(G\).
Reviewer: Wenhuai Shen (Guangzhou)
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