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Isomorphic Chevalley groups over integral domains. (English) Zbl 0831.14021

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)

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
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References:

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