## Isomorphisms of adjoint Chevalley groups over integral domains

HTML articles powered by AMS MathViewer

- by Yu Chen PDF
- Trans. Amer. Math. Soc.
**348**(1996), 521-541 Request permission

## Abstract:

It is shown that every automorphism of an adjoint Chevalley group over an integral domain containing the rational number field is uniquely expressible as the product of a ring automorphism, a graph automorphism and an inner automorphism while every isomorphism between simple adjoint Chevalley groups can be expressed uniquely as the product of a ring isomorphism, a graph isomorphism and an inner automorphism. The isomorphisms between the elementary subgroups are also found having analogous expressions.## References

- Paul C. Eklof and Alan H. Mekler,
*Almost free modules*, North-Holland Mathematical Library, vol. 46, North-Holland Publishing Co., Amsterdam, 1990. Set-theoretic methods. MR**1055083** - Armand Borel and Jacques Tits,
*Homomorphismes “abstraits” de groupes algébriques simples*, Ann. of Math. (2)**97**(1973), 499–571 (French). MR**316587**, DOI 10.2307/1970833 - N. Bourbaki,
*Éléments de mathématique. Fasc. XXXVII. Groupes et algèbres de Lie. Chapitre II: Algèbres de Lie libres. Chapitre III: Groupes de Lie*, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1349, Hermann, Paris, 1972. MR**0573068** - R. W. Carter and Y. Chen,
*Automorphisms of affine Kac-Moody groups and related Chevalley groups over rings*, J. Algebra**155**(1993), no. 1, 44–94. MR**1206622**, DOI 10.1006/jabr.1993.1031 - Y. Chen,
*Isomorphic Chevalley groups over integral domains*, Rend. Sem. Mat. Univ. Padova**92**(1994), 231–237. - H. S. Vandiver,
*Certain congruences involving the Bernoulli numbers*, Duke Math. J.**5**(1939), 548–551. MR**21**, DOI 10.1215/S0012-7094-39-00546-6 - M. Demazure, A. Grothendieck,
*Sch$\acute e$mas en groupes III*, Springer–Verlag, New York, 1970. - J. E. Humphreys,
*On the automorphisms of infinite Chevalley groups*, Canadian J. Math.**21**(1969), 908–911. MR**248143**, DOI 10.4153/CJM-1969-099-7 - Robert Steinberg,
*Automorphisms of finite linear groups*, Canadian J. Math.**12**(1960), 606–615. MR**121427**, DOI 10.4153/CJM-1960-054-6 - R. Steinberg,
*Lectures on Chevalley groups*, 1967. - Giovanni Taddei,
*Normalité des groupes élémentaires dans les groupes de Chevalley sur un anneau*, Applications of algebraic $K$-theory to algebraic geometry and number theory, Part I, II (Boulder, Colo., 1983) Contemp. Math., vol. 55, Amer. Math. Soc., Providence, RI, 1986, pp. 693–710 (French). MR**862660**, DOI 10.1090/conm/055.2/1862660

## Additional Information

**Yu Chen**- Affiliation: Department of Mathematics, University of Turin, Via Carlo Alberto 10, 10123 Torino, Italy
- Email: yuchen@dm.unito.it
- Received by editor(s): May 2, 1994
- Additional Notes: Supported in part by Italian M.U.R.S.T. research grant
- © Copyright 1996 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**348**(1996), 521-541 - MSC (1991): Primary 20G35, 20E36
- DOI: https://doi.org/10.1090/S0002-9947-96-01521-8
- MathSciNet review: 1329529