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Embeddings of
Authors:Carles Broto   Jesper M. Mø  ller
Affiliation:Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain ; Matematisk Institut, Universitetsparken 5, DK-2100 København Ø
Abstract:

We show that there is only one embedding of $mathrm Bmathrm{DI}_2$ in $mathrm Bmathrm{F}_4$ at the prime $p=3$, up to self-maps of $mathrm Bmathrm{DI}_2$. We also describe the effect of the group of self-equivalences of $mathrm Bmathrm{F}_4$ at the prime $p=3$ on this embedding and then show that the Friedlander exceptional isogeny composed with a suitable Adams map is an involution of $mathrm Bmathrm{F}_4$ whose homotopy fixed point set coincide with $mathrm Bmathrm{DI}_2$

Keywords:Homotopy Lie groups   Dickson algebra
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