Automorphisms of 𝐺𝐿_{𝑛}(𝑅),𝑅 a local ring

Pomfret, J.; McDonald, B. R.

doi:10.1090/S0002-9947-1972-0310087-X

Automorphisms of $\textrm {GL}_{n}(R), R$ a local ring
HTML articles powered by AMS MathViewer

by J. Pomfret and B. R. McDonald

Trans. Amer. Math. Soc. 173 (1972), 379-388

DOI: https://doi.org/10.1090/S0002-9947-1972-0310087-X

PDF | Request permission

Abstract:

Let $R$ denote a commutative local ring with maximal ideal $m$ and residue field $k = R/m$. In this paper we determine the group automorphisms of the general linear group $G{L_n}(R)$ when $n \geqslant 3$ and the characteristic of $k$ is not 2.

References

P. M. Cohn, On the structure of the $\textrm {GL}_{2}$ of a ring, Inst. Hautes Études Sci. Publ. Math. 30 (1966), 5–53. MR 207856, DOI 10.1007/BF02684355
Jean Dieudonné, On the automorphisms of the classical groups. With a supplement by Loo-Keng Hua, Mem. Amer. Math. Soc. 2 (1951), vi+122. MR 45125
L. K. Hua and I. Reiner, Automorphisms of the unimodular group, Trans. Amer. Math. Soc. 71 (1951), 331–348. MR 43847, DOI 10.1090/S0002-9947-1951-0043847-X
Wilhelm Klingenberg, Lineare Gruppen über lokalen Ringen, Amer. J. Math. 83 (1961), 137–153 (German). MR 124412, DOI 10.2307/2372725

Automorphisms of the sympletic group over a local ring

O. T. O’Meara, The automorphisms of the linear groups over any integral domain, J. Reine Angew. Math. 223 (1966), 56–100. MR 199278, DOI 10.1515/crll.1966.223.56
M. Ojanguren and R. Sridharan, A note on the fundamental theorem of projective geometry, Comment. Math. Helv. 44 (1969), 310–315. MR 242806, DOI 10.1007/BF02564531
Joseph Landin and Irving Reiner, Automorphisms of the general linear group over a principal ideal domain, Ann. of Math. (2) 65 (1957), 519–526. MR 87666, DOI 10.2307/1970063

Die Automorphismen der projektiven Gruppen

6

Yan Shi-jian, Linear groups over a ring, Chinese Math.—Acta 7 (1965), 163–179. MR 0222185