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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The normality of certain subgroups of elementary subgroups of Steinberg groups over rings


Author: James F. Hurley
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
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0330313-8
Keywords: Chevalley group, Steinberg group, elementary subgroup, root systems, Lie algebras
Article copyright: © Copyright 1974 American Mathematical Society