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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Chen, Yu 2000. Isomorphisms of Chevalley Groups over Algebras. Journal of Algebra, Vol. 226, Issue. 2, p. 719.

    Chen, Yu 1998. On minimal representations of simple algebraic groups over algebras. Communications in Algebra, Vol. 26, Issue. 2, p. 671.

  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 117, Issue 2
  • March 1995, pp. 203-212

On rational subgroups of reductive algebraic groups over integral domains

  • Yu Chen (a1)
  • DOI:
  • Published online: 24 October 2008

Let G and G′ be reductive algebraic groups defined over infinite fields k and k′ respectively. The purpose of this paper is to show that G and G′ have isomorphic root systems if their rational subgroups G(R) and G′(R′), where R and R′ are integral domains with Rk and R′ ⊇ k′, are isomorphic to each other, except in one particular case (see Theorem 3·4). This has been proved by R. Steinberg in [6, theorem 31] for simple Chevalley groups over perfect fields. In particular, when G and G′ are semisimple and adjoint, every isomorphism between G(R) and G′(R′) induces an isomorphism between their irreducible components (see Proposition 3·3). These results imply that, when G and G′ are semisimple k-groups and when both are either simply connected or adjoint, then they are isomorphic to each other as algebraic groups if and only if their rational subgroups over an integral domain that contains k are isomorphic to each other, except in one particular case (see Corollary 3·5).

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[1]A. Borel and J. Tits . Homomorphismes ‘abstraits’ de groupes algébriques simples. Ann. of Math. 97 (1973), 499571.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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