Chen, Yu Isomorphic Chevalley groups over integral domains. (English) Zbl 0831.14021 Rend. Semin. Mat. Univ. Padova 92, 231-237 (1994). Let \(G\) be a Chevalley-Demazure group scheme. It is well-known that, as a representable covariant functor from the category of commutative rings to the category of groups, \(G\) is uniquely determined by the semisimple complex Lie group \(G (\mathbb{C})\). The author generalizes this result for simple Chevalley-Demazure group schemes, as well as for absolutely almost simple algebraic groups, by replacing the complex field \(\mathbb{C}\) by an integral domain containing an infinite field. Reviewer: Li Fuan (Beijing) Cited in 1 ReviewCited in 14 Documents MSC: 14L15 Group schemes 20G35 Linear algebraic groups over adèles and other rings and schemes 13G05 Integral domains 20G15 Linear algebraic groups over arbitrary fields Keywords:representable covariant functor; category of commutative rings; category of groups; Lie group; simple Chevalley-Demazure group schemes; absolutely almost simple algebraic groups PDFBibTeX XMLCite \textit{Y. Chen}, Rend. Semin. Mat. Univ. Padova 92, 231--237 (1994; Zbl 0831.14021) Full Text: Numdam EuDML References: [1] E. Abe , Chevalley groups over local rings , Tôhoku Math. J. , ( 2 ) 21 ( 1969 ), pp. 477 - 494 . Article | MR 258837 | Zbl 0188.07201 · Zbl 0188.07201 · doi:10.2748/tmj/1178242958 [2] A. Borel , Linear Algebraic Groups , 2 nd edition, Springer-Verlag , New York ( 1991 ). MR 1102012 | Zbl 0726.20030 · Zbl 0726.20030 [3] A. Borel - J. TITS, Homomorphismes abstraits de groupes algébriques simples , Ann. Math. , 97 ( 1973 ), pp. 499 - 571 . MR 316587 | Zbl 0272.14013 · Zbl 0272.14013 · doi:10.2307/1970833 [4] C. Chevalley , Classification des groupes de Lie algébriques, Notes polycopiées , Inst. H. Poincaré , Paris ( 1956 -58). [5] C. Chevalley , Certains schemas de groupes semi-simples , Sem. Bourbaki , 13è année ( 1960 -61), exp. 219. Numdam | MR 1611814 | Zbl 0125.01705 · Zbl 0125.01705 [6] M. Demazure - A. GROTHENDIECK, Schémas en groupes III, Lect. Notes in Math ., 153, Springer-Verlag , Berlin -Heidelberg -New York ( 1970 ). MR 274458 | Zbl 0212.52810 · Zbl 0212.52810 · doi:10.1007/BFb0059027 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.