Isotypic rigidity conjecture for Chevalley groups

Let GΦ(R)G_\Phi(R) be a Chevalley group associated with a root system Φ\Phi over a ring RR, and let HH be a group isotypic to GΦ(R)G_\Phi(R). Isotypic rigidity conjecture for Chevalley groups. Then there is a ring SS such that HH is isomorphic to GΦ(S)G_\Phi(S) and RR and SS are isotypic rings. This refines the general rigidity question by predicting that isotypic Chevalley groups arise from isotypic coefficient rings, while the broader problem of classifying isotypic finitely generated groups remains open.

Sources & referencesView supporting material

Primary source

Eugene Plotkin, “On first order rigidity for linear groups”, arXiv:2010.03989 (2020).

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