Overgroups of subsystem subgroups in exceptional groups: a \(2A_1\)-proof. (English. Russian original) Zbl 07436571
St. Petersbg. Math. J. 32, No. 6, 1011-1031 (2021); translation from Algebra Anal. 32, No. 6, 72-100 (2021).
Summary: In the present paper, a weak form of sandwich classification for the overgroups of the subsystem subgroup \(E(\Delta ,R)\) of the Chevalley group \(G(\Phi ,R)\) is proved in the case where \(\Phi\) is a simply laced root system and \(\Delta\) is its sufficiently large subsystem. Namely, it is shown that, for such an overgroup \(H\), there exists a unique net of ideals \(\sigma\) of the ring \(R\) such that \(E(\Phi ,\Delta ,R,\sigma )\le H\le \operatorname{Stab}_{G(\Phi ,R)}(L(\sigma ))\), where \(E(\Phi ,\Delta ,R,\sigma )\) is an elementary subgroup associated with the net and \(L(\sigma )\) is the corresponding subalgebra of the Chevalley Lie algebra.
MSC:
| 20G15 | Linear algebraic groups over arbitrary fields |
Keywords:
Chevalley groups; commutative rings; exceptional groups; subsystem subgroups; subgroup latticeReferences:
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