Minimal representations for 6-dimensional nilpotent Lie algebra

被引：6
作者：
Rojas, Nadina [1 ,2 ]
机构：
[1] Univ Nacl Cordoba, CIEM CONICET, Cordoba, Argentina
[2] Univ Nacl Cordoba, FCEFyN, Cordoba, Argentina
来源：
JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2016年 / 15卷 / 10期
关键词：
Nilpotent Lie algebras; Ado's theorem; minimal faithful representation; nilrepresentation; FAITHFUL REPRESENTATIONS; ADOS THEOREM; REFINEMENT;
D O I：
10.1142/S0219498816501917
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Given a Lie algebra g, let mu(g) and mu nil(g) be the minimal dimension of a faithful representation and nilrepresentation of g, respectively. In this paper, we give mu(g) and mu nil(g) for each nilpotent Lie algebra g of dimension 6 over a field K of characteristic zero. We also give a minimal faithful representation and nilrepresentation in each case.
引用
收藏
页数：19
相关论文
共 19 条
[1]  
Benjumea JC, 2008, MATH SCAND, V102, P17
[2]  
BENOIST Y, 1995, J DIFFER GEOM, V41, P21
[3]   On a refinement of Ado's theorem [J].
Burde, D .
ARCHIV DER MATHEMATIK, 1998, 70 (02) :118-127
[4]   Minimal faithful representations of reductive Lie algebras [J].
Burde, Dietrich ;
Moens, Wolfgang .
ARCHIV DER MATHEMATIK, 2007, 89 (06) :513-523
[5]   Faithful Lie algebra modules and quotients of the universal enveloping algebra [J].
Burde, Dietrich ;
Moens, Wolfgang Alexander .
JOURNAL OF ALGEBRA, 2011, 325 (01) :440-460
[6]   Computing faithful representations for nilpotent Lie algebras [J].
Burde, Dietrich ;
Eick, Bettina ;
de Graaf, Willem .
JOURNAL OF ALGEBRA, 2009, 322 (03) :602-612
[7]   FAITHFUL REPRESENTATIONS OF MINIMAL DIMENSION OF CURRENT HEISENBERG LIE ALGEBRAS [J].
Cagliero, Leandro ;
Rojas, Nadina .
INTERNATIONAL JOURNAL OF MATHEMATICS, 2009, 20 (11) :1347-1362
[8]  
de Graaf W, 1997, P 1997 INT S SYMB AL, P54
[9]   Classification of 6-dimensional nilpotent Lie algebras over fields of characteristic not 2 [J].
de Graaf, Willem A. .
JOURNAL OF ALGEBRA, 2007, 309 (02) :640-653
[10]  
Ghanam R., 2006, Hadronic J, V29, P299
12