Defining R and G(R)
<p>We show that for Chevalley groups G(R)G(R) of rank at least 2 over an integral domain RR each root subgroup is (essentially) the double centralizer of a corresponding root element. In many cases, this implies that RR and G(R)G(R) are bi-interpretable, yielding a new approach to bi-interpret...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
| Published: |
EMS Press
2022
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| Summary: | <p>We show that for Chevalley groups G(R)G(R) of rank at least 2 over an integral domain RR each root subgroup is (essentially) the double centralizer of a corresponding root element. In many cases, this implies that RR and G(R)G(R) are bi-interpretable, yielding a new approach to bi-interpretability for algebraic groups over a wide range of rings and fields.</p>
<p>For such groups it then follows that the group G(R)G(R) is (finitely) axiomatizable in the appropriate class of groups provided RR is (finitely) axiomatizable in the corresponding class of rings.</p> |
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