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Transactions of the American Mathematical Society

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Embeddings of $\mathrm{DI}_2$ in $\mathrm{F}_4$


Authors: Carles Broto and Jesper M. Møller
Journal: Trans. Amer. Math. Soc. 353 (2001), 4461-4479
MSC (1991): Primary 55R35, 55P15, 55P10
DOI: https://doi.org/10.1090/S0002-9947-01-02781-7
Published electronically: May 3, 2001
MathSciNet review: 1851179
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Abstract:

We show that there is only one embedding of $\mathrm B\mathrm{DI}_2$ in $\mathrm B\mathrm{F}_4$ at the prime $p=3$, up to self-maps of $\mathrm B\mathrm{DI}_2$. We also describe the effect of the group of self-equivalences of $\mathrm B\mathrm{F}_4$ 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 $\mathrm B\mathrm{F}_4$ whose homotopy fixed point set coincide with $\mathrm B\mathrm{DI}_2$


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Additional Information

Carles Broto
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain
Email: broto@mat.uab.es

Jesper M. Møller
Affiliation: Matematisk Institut, Universitetsparken 5, DK-2100 København Ø
Email: moller@math.ku.dk

DOI: https://doi.org/10.1090/S0002-9947-01-02781-7
Keywords: Homotopy Lie groups, Dickson algebra
Received by editor(s): May 4, 1999
Published electronically: May 3, 2001
Additional Notes: C. Broto is partially supported by DGES grant 97-0203
Article copyright: © Copyright 2001 American Mathematical Society

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