Isomorphism and Isotopism Classes of Filiform Lie Algebras of Dimension up to Seven Over Finite Fields

被引：0
作者：
O. J. Falcón
R. M. Falcón
J. Núñez
机构：
[1] University of Seville,Department of Geometry and Topology, Faculty of Mathematics
[2] University of Seville,Department of Applied Mathematics I, School of Building Engineering
来源：
Results in Mathematics | 2017年 / 71卷
关键词：
Filiform Lie algebra; finite field; isotopism; isomorphism; 17B60; 68W30;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper deals with a new series of isotopism invariants that enable us to determine explicitly the distribution of n-dimensional filiform Lie algebras into isomorphism and isotopism classes. For n≤6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\le 6$$\end{document}, this distribution is explicitly obtained over any field. For n=7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=7$$\end{document}, this is determined over algebraically closed fields and over finite fields.
引用
收藏
页码：1151 / 1166
页数：15
相关论文
共 26 条
[1]  
Albert AA(1942)Non-associative algebras: I. Fundamental concepts and isotopy Ann. Math. Second Ser. 43 685-707
[2]  
Allison B(2009)Multiloop realization of extended affine Lie algebras and Lie tori Trans. Am. Math. Soc. 361 4807-4842
[3]  
Berman S(1989)Classification des algèbres de Lie nilpotentes complexes de dimension 7 Archiv der Mathematik 52 175-185
[4]  
Faulkner J(1997)Isotopy and identities in alternative algebras Proc. Am. Math. Soc. 125 1571-1575
[5]  
Pianzola A(2003)Complex filiform Lie algebras of dimension 11 Appl. Math. Comput. 141 611-630
[6]  
Ancochéa-Bermúdez JM(1944)Some results in the theory of linear non-associative algebras Trans. Am. Math. Soc. 56 141-199
[7]  
Goze M(2012)Six-dimensional nilpotent Lie algebras Linear Algebra Appl. 436 163-189
[8]  
Babikov M(1996)Study of two invariants in complex filiform Lie algebras Algebras Groups Geom. 13 55-70
[9]  
Boza L(2007)Classification of 6-dimensional nilpotent Lie algebras over fields of characteristic not 2 J. Algebra 309 640-653
[10]  
Fedriani EM(2008)Ternary derivations of finite-dimensional real division algebras Linear Algebra Appl. 428 2192-2219
123