Linear Bundle of Lie Algebras Applied to the Classification of Real Lie Algebras

Symmetry

Karolina Wojciechowicz¹  Alina Dobrogowska¹ 

[1] Faculty of Mathematics, University of Bialystok, Ciołkowskiego 1M, 15-245 Białystok, Poland;

关键词: Lie algebra;    linear bundle of Lie algebras;    quasisimple orthogonal algebra;    Poisson manifold;    bi-Hamiltonian structure;   

DOI  :  10.3390/sym13081455

来源: DOAJ

【 摘 要 】

We present a new look at the classification of real low-dimensional Lie algebras based on the notion of a linear bundle of Lie algebras. Belonging to a suitable family of Lie bundles entails the compatibility of the Lie–Poisson structures with the dual spaces of those algebras. This gives compatibility of bi-Hamiltonian structure on the space of upper triangular matrices and with a bundle at the algebra level. We will show that all three-dimensional Lie algebras belong to two of these families and four-dimensional Lie algebras can be divided in three of these families.

【 授权许可】

Unknown