A solvability criterion for the Lie algebra of derivations of a fat point

被引：5
|
作者：
Schulze, Mathias [1 ]
机构：
[1] Oklahoma State Univ, Dept Math, Stillwater, OK 74078 USA
来源：
JOURNAL OF ALGEBRA | 2010年 / 323卷 / 10期
关键词：
Fat point; Derivation; Lie algebra; Solvability; Hypersurface singularity; Milnor algebra; Tyurina algebra; Yau algebra;
D O I：
10.1016/j.jalgebra.2010.01.010
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider the Lie algebra of derivations of a zero-dimensional local complex algebra. We describe an inequality involving the embedding dimension, the order, and the first deviation that forces this Lie algebra to be solvable. Our result was motivated by and generalizes the solvability of the Yau algebra of an isolated hypersurface singularity. (C) 2010 Elsevier Inc. All rights reserved.
引用
收藏
页码：2916 / 2921
页数：6
相关论文
共 50 条
  • [1] A CRITERION FOR THE SOLVABILITY OF A FINITE-DIMENSIONAL LIE-ALGEBRA
    KOSTRIKIN, AI
    VESTNIK MOSKOVSKOGO UNIVERSITETA SERIYA 1 MATEMATIKA MEKHANIKA, 1982, (02): : 5 - 8
  • [2] The Lie algebra of derivations of a current Lie algebra
    Ochoa Arango, Jesus Alonso
    Rojas, Nadina
    COMMUNICATIONS IN ALGEBRA, 2020, 48 (02) : 625 - 637
  • [3] Algebra of derivations of Lie algebras
    Camacho, LM
    Gómez, JR
    Navarro, RM
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2001, 332 : 371 - 380
  • [4] ALGEBRAIC LIE ALGEBRA BUNDLES AND DERIVATIONS OF LIE ALGEBRA BUNDLES
    Monica, M., V
    Rajendra, R.
    INTERNATIONAL ELECTRONIC JOURNAL OF ALGEBRA, 2024, 35 : 95 - 107
  • [5] On automorphisms and derivations of a Lie algebra
    Varea, VR
    Varea, JJ
    ALGEBRA COLLOQUIUM, 2006, 13 (01) : 119 - 132
  • [6] Lie Algebra of Derivations of the Algebra of Differential Operators
    赵开明
    ChineseScienceBulletin, 1993, (10) : 793 - 798
  • [7] DERIVATIONS OF THE LIE-ALGEBRA STRUCTURE OF THE ENVELOPING ALGEBRA OF A SEMISIMPLE LIE-ALGEBRA
    DEWILDE, M
    JASON, A
    MUKILA, PMW
    TOUSSET, E
    VANHAUTEN, F
    COCAIKO, J
    COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1995, 320 (11): : 1299 - 1304
  • [8] On the Lie algebra structure of integrable derivations
    Briggs, Benjamin
    Degrassi, Lleonard Rubio y
    BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2023, 55 (06) : 2617 - 2634
  • [9] ON THE IDEALS OF A LIE-ALGEBRA OF DERIVATIONS
    JORDAN, DA
    JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1986, 33 : 33 - 39
  • [10] DERIVATIONS AND EXTENSIONS OF LIE COLOR ALGEBRA
    张庆成
    张永正
    ActaMathematicaScientia, 2008, (04) : 933 - 948
12345