We study an infinite-dimensional Lie algebra B, called local area-preserving algebra for the Klein bottle introduced by C. Pope and L. Romans [Class. Quantum Grav. 7 (1990) 79--109]. We show that B is a finitely generated simple Lie algebra with a unique (up to scalars) symmetric invariant bilinear form. The derivation algebra and the universal central extension of B are also determined.
Classification :
17B65, 17B68
Mots-clés :
Lie algebra, Klein bottle, Invariant bilinear form, central extension, derivation
Affiliations des auteurs :
Cuipo Jiang
1
;
Jingjing Jiang
1
;
Yufeng Pei
2
1
Dept. of Mathematics, Shanghai Jiaotong University, No. 800 Dongchuan Road, Shanghai, P.R.China 200240
2
Dept. of Mathematics, Shanghai Normal University, No. 100 Guilin Road, Shanghai, P.R.China 200234
Cuipo Jiang; Jingjing Jiang; Yufeng Pei. Structure of the Local Area-Preserving Lie Algebra for the Klein Bottle. Journal of Lie Theory, Tome 21 (2011) no. 1, pp. 101-122. http://geodesic.mathdoc.fr/item/JOLT_2011_21_1_a4/
@article{JOLT_2011_21_1_a4,
author = {Cuipo Jiang and Jingjing Jiang and Yufeng Pei},
title = {Structure of the {Local} {Area-Preserving} {Lie} {Algebra} for the {Klein} {Bottle}},
journal = {Journal of Lie Theory},
pages = {101--122},
year = {2011},
volume = {21},
number = {1},
url = {http://geodesic.mathdoc.fr/item/JOLT_2011_21_1_a4/}
}
TY - JOUR
AU - Cuipo Jiang
AU - Jingjing Jiang
AU - Yufeng Pei
TI - Structure of the Local Area-Preserving Lie Algebra for the Klein Bottle
JO - Journal of Lie Theory
PY - 2011
SP - 101
EP - 122
VL - 21
IS - 1
UR - http://geodesic.mathdoc.fr/item/JOLT_2011_21_1_a4/
ID - JOLT_2011_21_1_a4
ER -
%0 Journal Article
%A Cuipo Jiang
%A Jingjing Jiang
%A Yufeng Pei
%T Structure of the Local Area-Preserving Lie Algebra for the Klein Bottle
%J Journal of Lie Theory
%D 2011
%P 101-122
%V 21
%N 1
%U http://geodesic.mathdoc.fr/item/JOLT_2011_21_1_a4/
%F JOLT_2011_21_1_a4
