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Rational Conjugacy Classes of Maximal Tori in Groups of Type $D_{n}$

Mathematics and Computer Science, C524 University Hall, 4401 University Drive, University of Lethbridge, Lethbridge, Alberta, T1K 3M4, Canada

E-mail Address: andrew.fiori@uleth.ca

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https://doi.org/10.1142/S0219498821500638Cited by:1 (Source: Crossref)

Abstract

We give a concrete characterization of the rational conjugacy classes of maximal tori in groups of type $D_{n}$ , with specific emphasis on the case of number fields and $p$ -adic fields. This includes the forms associated to quadratic spaces, all of their inner and outer forms as well as the Spin groups, their simply connected covers. In particular, in this work, we handle all (simply connected) outer forms of $D_{4}$ .

Communicated by S. K. Jain

Keywords:

AMSC: 11E72, 11E57

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