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- Title
Defining R and G(R).
- Authors
Segal, Dan; Tent, Katrin
- Abstract
We show that for Chevalley groups G(R) of rank at least 2 over an integral domain R each root subgroup is (essentially) the double centralizer of a corresponding root element. In many cases, this implies that R and G(R) are bi-interpretable, yielding a new approach to biinterpretability 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.
- Subjects
CHEVALLEY groups; LINEAR algebraic groups; RING theory; ROOTS of equations; ALGEBRAIC varieties
- Publication
Journal of the European Mathematical Society (EMS Publishing), 2023, Vol 25, Issue 8, p3325
- ISSN
1435-9855
- Publication type
Article
- DOI
10.4171/JEMS/1255