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arXiv · 2004.13407

Defining R and G(R)

Dan Segal·Katrin Tent
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Abstract

We show that for Chevalley groups G(R) of rank at least 2 over a ring R the root subgroups are essentially (nearly always) the double centralizers of corresponding root elements. In very many cases this implies that R and G(R) are bi-interpretable, yielding a new approach to bi-interpretability for algebraic groups over a wide range of rings and fields. For such groups it then follows that the group G(R) is finitely axiomatizable in the appropriate class of groups provided R is finitely axiomatizable in the corresponding class of rings.

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Dan Segal, Katrin Tent. 2020-04-28. Defining R and G(R). https://arxiv.org/abs/2004.13407

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