Next Article in Journal
Effects of Anodic Aluminum Oxide Substrate Pore Geometry on the Gas-Phase Photocatalytic Activity of ZnO/Al2O3 Composites Prepared by Atomic Layer Deposition
Previous Article in Journal
Network Intrusion Detection Based on an Efficient Neural Architecture Search
Previous Article in Special Issue
Domination in Join of Fuzzy Incidence Graphs Using Strong Pairs with Application in Trading System of Different Countries
Article

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

Faculty of Mathematics, University of Bialystok, Ciołkowskiego 1M, 15-245 Białystok, Poland
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editor: José Carlos R. Alcantud
Symmetry 2021, 13(8), 1455; https://doi.org/10.3390/sym13081455
Received: 26 June 2021 / Revised: 5 August 2021 / Accepted: 5 August 2021 / Published: 9 August 2021
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. View Full-Text
Keywords: Lie algebra; linear bundle of Lie algebras; quasisimple orthogonal algebra; Poisson manifold; bi-Hamiltonian structure Lie algebra; linear bundle of Lie algebras; quasisimple orthogonal algebra; Poisson manifold; bi-Hamiltonian structure
MDPI and ACS Style

Dobrogowska, A.; Wojciechowicz, K. Linear Bundle of Lie Algebras Applied to the Classification of Real Lie Algebras. Symmetry 2021, 13, 1455. https://doi.org/10.3390/sym13081455

AMA Style

Dobrogowska A, Wojciechowicz K. Linear Bundle of Lie Algebras Applied to the Classification of Real Lie Algebras. Symmetry. 2021; 13(8):1455. https://doi.org/10.3390/sym13081455

Chicago/Turabian Style

Dobrogowska, Alina, and Karolina Wojciechowicz. 2021. "Linear Bundle of Lie Algebras Applied to the Classification of Real Lie Algebras" Symmetry 13, no. 8: 1455. https://doi.org/10.3390/sym13081455

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop