Open AccessClassification of 5-dimentional subalgebras for 6-dimentional nilpotent Lie algebras
Author(s) -
В. Л. Штукарь
Publication year - 2020
Publication title -
vescì nacyânalʹnaj akadèmìì navuk belarusì. seryâ fìzìka-matèmatyčnyh navuk
Language(s) - English
Resource type - Journals
eISSN - 2524-2415
pISSN - 1561-2430
DOI - 10.29235/1561-2430-2020-56-2-175-188
Subject(s) - mathematics , linear subspace , lie algebra , pure mathematics , isomorphism (crystallography) , nilpotent , adjoint representation of a lie algebra , non associative algebra , adjoint representation , lie conformal algebra , algebra over a field , chemistry , crystal structure , crystallography
In this paper, we consider the classical problem of the classification of subalgebras of small dimensional Lie algebras. We found all 5-dimentional subalgebras of 6-dimentional nilpotent Lie algebras under the field with the zero characteristic. As is known, up to isomorphism all 6-dimensional nilpotent Lie algebras (their number is 32) were received by V. V. Morosov. However, the standard method based on the Campbell – Hausdorf formula is not effective for the determination of subalgebras of Lie 5- or higher dimensional algebras. In our research, we use a new approach to the solution of the problem of the determination of 5-dimensional subalgeras of indicated 6-dimensional nilpotent Lie algerbas, namely, the application of canonical bases for subspaces of vector spaces.