$k$-regular elements in semisimple algebraic groups
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- by Peter P. Andre PDF
- Trans. Amer. Math. Soc. 201 (1975), 105-124 Request permission
Abstract:
In this paper, Steinberg’s concept of a regular element in a semisimple algebraic group defined over an algebraically closed field is generalized to the concept of a $k$-regular element in a semisimple algebraic group defined over an arbitrary field of characteristic zero. The existence of semisimple and unipotent $k$-regular elements in a semisimple algebraic group defined over a field of characteristic zero is proved. The structure of all $k$-regular unipotent elements is given. The number of minimal parabolic subgroups containing a $k$-regular element is given. The number of conjugacy classes of $R$-regular unipotent elements is given, where $R$ is the real field. The number of conjugacy classes of ${Q_p}$-regular unipotent elements is shown to be finite, where ${Q_p}$ is the field of $p$-adic numbers.References
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Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 201 (1975), 105-124
- MSC: Primary 20G30; Secondary 20G20
- DOI: https://doi.org/10.1090/S0002-9947-1975-0357637-8
- MathSciNet review: 0357637