Journal
JOURNAL OF GEOMETRY AND PHYSICS
Volume 170, Issue -, Pages -Publisher
ELSEVIER
DOI: 10.1016/j.geomphys.2021.104384
Keywords
Leibniz algebra; Nilpotent algebra; Grading; Automorphism; Torus
Categories
Funding
- PCI of the UCA 'Teoria de Lie y Teoria de Espacios de Banach'
- PAI [FQM298, FQM7156]
- Ministerio de Economia y Competitividad (Spain) (AEI/FEDER, UE) [MTM2016-79661-P, MTM2013-41208P]
- 2014-2020 ERDF Operational Programme
- Department of Economy, Knowledge, Business and University of the Regional Government of Andalusia [FEDER-UCA18-107643]
- RFBR [20-01-00030]
- CNPq [302980/2019-9]
- FCT [UIDB/MAT/00212/2020, UIDP/MAT/00212/2020]
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This study classifies all abelian group gradings on null-filiform and one-parametric filiform Leibniz algebras up to equivalences. It is found that any grading on a null-filiform Leibniz algebra is toral, while non-toral gradings exist on one-parametric filiform Leibniz algebras.
We classify, up to equivalences, all abelian groups gradings on null-filiform and one-parametric filiform Leibniz algebras. Any grading on a null-filiform Leibniz algebra is toral but there are non-toral gradings on one-parametric filiform Leibniz algebras. (C) 2021 Elsevier B.V. All rights reserved.
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