PreprintarXiv licencearXiv
On nilpotent Lie algebras arising from parabolic subalgebras and quivers --- three-step cases
Abstract
Nilpotent Lie groups are important subjects for studying spacial left-invariant geometric structures. However, nilpotent Lie groups are impossible to classify, and even the two-step case has not been classified. There are several classes of examples of nilpotent Lie algebras that arise with higher nilpotency steps. In this paper, we focus on two of these methods. The first one is the nilpotent parts of parabolic subalgebras of semisimple Lie algebras. The second one is the nilpotent Lie algebras obtained by quivers. We list and compare nilpotent Lie algebras obtained by these two methods that are three-step and of dimension at most 10.
Related
- Intermediate subalgebras of cross-product von Neumann algebras arising from weakly compact actions
- Two-step nilpotent Lie algebras obtained by quivers and geometric structures
- On the structure of polynomial multicorrelation sequences arising from nilpotent actions
- Borel subalgebras of Lie algebras of vector fields
- Resolution quivers and the QF-1 property of higher Auslander Nakayama algebras
BibTeX
@misc{mizoguchi2026nilpotent,
title = {{On nilpotent Lie algebras arising from parabolic subalgebras and quivers --- three-step cases}},
author = {Fumika Mizoguchi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25903},
eprint = {2610.25903},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25903},
}
RIS
TY - UNPB
TI - On nilpotent Lie algebras arising from parabolic subalgebras and quivers --- three-step cases
AU - Fumika Mizoguchi
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.25903
UR - https://arxiv.org/abs/2610.25903
AB - Nilpotent Lie groups are important subjects for studying spacial left-invariant geometric structures. However, nilpotent Lie groups are impossible to classify, and even the two-step case has not been classified. There are several classes of examples of nilpotent Lie algebras that arise with higher nilpotency steps. In this paper, we focus on two of these methods. The first one is the nilpotent parts of parabolic subalgebras of semisimple Lie algebras. The second one is the nilpotent Lie algebras obtained by quivers. We list and compare nilpotent Lie algebras obtained by these two methods that are three-step and of dimension at most 10.
ER -