The normality of certain subgroups of elementary subgroups of Steinberg groups over rings
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- by James F. Hurley
- Proc. Amer. Math. Soc. 42 (1974), 377-380
- DOI: https://doi.org/10.1090/S0002-9939-1974-0330313-8
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Abstract:
This paper amends the approach used in an earlier paper to construct, from ideals in the Chevalley algebra ${L_R}$ over a commutative ring R with identity, normal subgroups of the elementary subgroup $G_R^1$ of Steinberg’s twisted group corresponding to L, a finite dimensional simple Lie algebra over the complex field. The set of normal subgroups so constructed turns out to be in one-to-one correspondence with the set of equivalence classes of ideals of R under an equivalence relation defined in terms of the underlying automorphism of R of order 2.References
- James F. Hurley, Ideals in Chevalley algebras, Trans. Amer. Math. Soc. 137 (1969), 245–258. MR 237589, DOI 10.1090/S0002-9947-1969-0237589-9
- James F. Hurley, Some normal subgroups of elementary subgroups of Chevalley groups over rings, Amer. J. Math. 93 (1971), 1059–1069. MR 306352, DOI 10.2307/2373745
- James F. Hurley, Normality and terminality in the elementary subgroups of Steinberg groups over rings, Proc. Amer. Math. Soc. 34 (1972), 30–34. MR 299692, DOI 10.1090/S0002-9939-1972-0299692-2
- Wilhelm Klingenberg, Lineare Gruppen über lokalen Ringen, Amer. J. Math. 83 (1961), 137–153 (German). MR 124412, DOI 10.2307/2372725
- W. R. Scott, Group theory, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. MR 0167513
- Robert Steinberg, Variations on a theme of Chevalley, Pacific J. Math. 9 (1959), 875–891. MR 109191 —, Lectures on Chevalley groups, Mathematics Dept., Yale University, New Haven, Conn., 1967/68.
Bibliographic Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 42 (1974), 377-380
- MSC: Primary 20G35
- DOI: https://doi.org/10.1090/S0002-9939-1974-0330313-8
- MathSciNet review: 0330313