TOWERS OF DERIVATION FOR LIE RINGS AND SOME RESULTS ON COMPLETE LIE RINGS

被引：0
|
作者：
Liao Jun [1 ]
Zheng Dabin [1 ]
Liu Heguo [1 ]
机构：
[1] Hubei Univ, Fac Math & Comp Sci, Wuhan 430062, Peoples R China
来源：
ACTA MATHEMATICA SCIENTIA | 2010年 / 30卷 / 05期
关键词：
Lie rings; derivation towers; complete Lie rings; ALGEBRAS;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The well-known tower theorem of groups (resp. Lie algebras) shows that the tower of automorphism groups (resp. derivation algebras) of a finite group (resp. a finite dimensional Lie algebra) with trivial center terminates after finitely many steps. We generalize these results for Lie rings, and present some necessary and sufficient conditions for Lie rings to be complete.
引用
收藏
页码：1769 / 1775
页数：7
相关论文
共 50 条
  • [31] Some results on complete Lie superalgebras
    Wang, LY
    Meng, DJ
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2002, 355 : 1 - 14
  • [32] Multiplicative Lie triple derivation of triangular 3-matrix rings
    Jabeen A.
    Ahmad M.
    ANNALI DELL'UNIVERSITA' DI FERRARA, 2021, 67 (2) : 293 - 308
  • [33] Lie algebras and Lie groups over noncommutative rings
    Berenstein, Arkady
    Retakh, Vladimir
    ADVANCES IN MATHEMATICS, 2008, 218 (06) : 1723 - 1758
  • [34] On the Lie derivations and generalized Lie derivations of quaternion rings
    Ghahramani, H.
    Ghosseiri, M. N.
    Zadeh, L. Heidari
    COMMUNICATIONS IN ALGEBRA, 2019, 47 (03) : 1215 - 1221
  • [35] LIE ISOMORPHISMS OF SIMPLE RINGS
    MARTINDALE, WS
    JOURNAL OF THE LONDON MATHEMATICAL SOCIETY, 1969, 44 (174P): : 213 - +
  • [36] A CLASS OF LIE ADMISSIBLE RINGS
    KLEINFELD, E
    KLEINFELD, M
    COMMUNICATIONS IN ALGEBRA, 1985, 13 (02) : 465 - 477
  • [37] On Lie rings of torsion groups
    Martinez, Consuelo
    Zelmanov, Efim
    BULLETIN OF MATHEMATICAL SCIENCES, 2016, 6 (03) : 371 - 377
  • [38] INVARIANTS OF FREE LIE RINGS
    BURROW, MD
    COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1958, 11 (04) : 419 - 431
  • [39] Representation rings of Lie superalgebras
    Landweber, Gregory D.
    K-THEORY, 2005, 36 (1-2): : 115 - 168
  • [40] Lie maps on alternative rings
    Bruno Leonardo Macedo Ferreira
    Henrique Guzzo
    Bollettino dell'Unione Matematica Italiana, 2020, 13 : 181 - 192
12345