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Dear authors! Submission of all materials is carried out only electronically through Online Submission System in personal account. DOI: 10.46698/i774606368062u On Irreducible Carpets of Additive Subgroups of Type \(F_4\)
Likhacheva, A. O.
Vladikavkaz Mathematical Journal 2023. Vol. 25. Issue 2.
Abstract:
The article describes irreducible carpets \(\mathfrak{A}=\{\mathfrak{A}_r:\ r\in \Phi\}\) of type \(F_4\) over the field \(K\), all of whose additive subgroups \(\mathfrak{A}_r\) are \(R\)modules, where \(K\) is an algebraic extension of the field \(R\). An interesting fact is that carpets which are parametrized by a pair of additive subgroups appear only in characteristic 2. Up to conjugation by a diagonal element from the corresponding Chevalley group, this pair of additive subgroups becomes fields, but they may be different. In addition, we establish that such carpets \(\mathfrak{A}\) are closed. Previously, V. M. Levchuk described irreducible Lie type carpets of rank greater than 1 over the field \(K\), at least one of whose additive subgroups is an \(R\)module, where \(K\) is an algebraic extension of the field \(R\), under the assumption that the characteristic of the field \(K\) is different from 0 and 2 for types \(B_l\), \(C_l\), \(F_4\), while for type \(G_2\) it is different from 0, 2, and 3 [1]. For these characteristics, up to conjugation by a diagonal element, all additive subgroups of such carpets coincide with one intermediate subfield between \(R\) and \(K\).
Keywords: Chevalley group, carpet of additive subgroups, carpet subgroup, commutative ring.
Language: Russian
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For citation: Likhacheva, A. O. On Irreducible Carpets of Additive Subgroups of Type \(F_4\), Vladikavkaz Math. J., 2023, vol. 25, no. 2, pp. 117123 (in
Russian). DOI 10.46698/i774606368062u ← Contents of issue 
 

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