The algebraic and geometric classification of nilpotent left-symmetric algebras
Abstract
This paper is devoted to the complete algebraic and geometric classification of complex 4-dimensional nilpotent left-symmetric algebras. The corresponding geometric variety has dimension 15 and decomposes into 3 irreducible components determined by the Zariski closures of two one-parameter families of algebras and a two-parameter family of algebras (see Theorem B). In particular, there are no rigid 4-dimensional complex nilpotent left symmetric algebras.
- Publication:
-
Journal of Geometry and Physics
- Pub Date:
- September 2021
- DOI:
- 10.1016/j.geomphys.2021.104287
- arXiv:
- arXiv:2106.00336
- Bibcode:
- 2021JGP...16704287A
- Keywords:
-
- 17D25;
- 17A30;
- 14D06;
- 14L30;
- Mathematics - Rings and Algebras
- E-Print:
- arXiv admin note: substantial text overlap with arXiv:1912.02691, arXiv:1812.01442, arXiv:2004.03598, arXiv:1902.01706