Infinitesimal deformations of naturally graded filiform Leibniz algebras
Abstract
In the present paper we describe infinitesimal deformations of complex naturally graded filiform Leibniz algebras. It is known that any n-dimensional filiform Lie algebra can be obtained by a linear integrable deformation of the naturally graded algebra Fn3(0) . We establish that in the same way any n-dimensional filiform Leibniz algebra can be obtained by an infinitesimal deformation of the filiform Leibniz algebras Fn1,Fn2and Fn3(α) . Moreover, we describe the linear integrable deformations of the above-mentioned algebras with a fixed basis of HL2 in the set of all n-dimensional Leibniz algebras. Among these deformations one new rigid algebra has been found.
- Publication:
-
Journal of Geometry and Physics
- Pub Date:
- December 2014
- DOI:
- 10.1016/j.geomphys.2014.07.034
- arXiv:
- arXiv:1305.2676
- Bibcode:
- 2014JGP....86..149K
- Keywords:
-
- 17A32;
- 17A70;
- 17B30;
- 13D10;
- 16S80;
- Mathematics - Algebraic Geometry;
- Mathematics - Rings and Algebras;
- 17A32;
- 17A70;
- 17B30;
- 13D10;
- 16S80
- E-Print:
- 16 pages