Lie algebras admitting a metacyclic Frobenius group of automorphisms
| Autor: | Makarenko, N. Yu., Khukhro, E. I. |
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| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | Siberian Mathematical Journal January 2013, Volume 54, Issue 1, pp 99-113 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1134/S0037446613010138 |
| Popis: | Suppose that a Lie algebra $L$ admits a finite Frobenius group of automorphisms $FH$ with cyclic kernel $F$ and complement $H$ such that the characteristic of the ground field does not divide $|H|$. It is proved that if the subalgebra $C_L(F)$ of fixed points of the kernel has finite dimension $m$ and the subalgebra $C_L(H)$ of fixed points of the complement is nilpotent of class $c$, then $L$ has a nilpotent subalgebra of finite codimension bounded in terms of $m$, $c$, $|H|$, and $|F|$ whose nilpotency class is bounded in terms of only $|H|$ and $c$. Examples show that the condition of the kernel $F$ being cyclic is essential. Comment: 19 pages, to appear in Siberian Mathematical Journal, Vol.54 (2013), No. 1. arXiv admin note: substantial text overlap with arXiv:1301.3409 |
| Databáze: | arXiv |
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