Embeddings of \(\text{DI}_2\) in \(\text{F}_4\) (Q2731952)
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scientific article; zbMATH DE number 1626825
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Embeddings of \(\text{DI}_2\) in \(\text{F}_4\) |
scientific article; zbMATH DE number 1626825 |
Statements
30 July 2001
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homotopy Lie groups
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Dickson algebra
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Embeddings of \(\text{DI}_2\) in \(\text{F}_4\) (English)
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The Dickson algebra of invariants of the \(GL_2(\mathbb{F}_3)\) action on \(\mathbb{F}_3[t_1,t_3]\) is \(D(2)\cong \mathbb{F}_3[x_{12},x_{16}]\). Zabrodsky constructed a space \(BDI_2\) realizing \(D(2)\) in \(\text{mod }3\) cohomology. The construction, quite technical, involved \(BF_4\), the classifying space of the exceptional Lie group \(F_4\).NEWLINENEWLINENEWLINEThe authors construct an involution on \(BF_4\) which yields \(BDI_2\) as the homotopy fixed point space of the action on \(BF_4\). Up to self maps of \(BDI_2\), there is only a single embedding of \(BDI_2\) in \(BF_4\).
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