2021
del Barco, Viviana; Moroianu, Andrei; Raffero, Alberto
Purely coclosed G2-structures on 2-step nilpotent Lie groups Journal Article
Em: Revista Matemática Complutense, vol. 35, pp. 323–359, 2021.
Resumo | Links | BibTeX | Tags: 2-Step nilpotent Lie algebra, G2-Strominger system, Metric Lie algebra, Purely coclosed G2-structure
@article{nokey,
title = {Purely coclosed G2-structures on 2-step nilpotent Lie groups},
author = {Viviana del Barco and Andrei Moroianu and Alberto Raffero},
url = {https://link.springer.com/article/10.1007/s13163-021-00392-0},
doi = {https://doi.org/10.1007/s13163-021-00392-0},
year = {2021},
date = {2021-04-02},
journal = {Revista Matem\'{a}tica Complutense},
volume = {35},
pages = {323\textendash359},
abstract = {We consider left-invariant (purely) coclosed G2-structures on 7-dimensional 2-step nilpotent Lie groups. According to the dimension of the commutator subgroup, we obtain various criteria characterizing the Riemannian metrics induced by left-invariant purely coclosed G2-structures. Then, we use them to determine the isomorphism classes of 2-step nilpotent Lie algebras admitting such type of structures. As an intermediate step, we show that every metric on a 2-step nilpotent Lie algebra admitting coclosed G2-structures is induced by one of them. Finally, we use our results to give the explicit description of the metrics induced by purely coclosed G2-structures on 2-step nilpotent Lie algebras with derived algebra of dimension at most two, up to automorphism.},
keywords = {2-Step nilpotent Lie algebra, G2-Strominger system, Metric Lie algebra, Purely coclosed G2-structure},
pubstate = {published},
tppubtype = {article}
}
We consider left-invariant (purely) coclosed G2-structures on 7-dimensional 2-step nilpotent Lie groups. According to the dimension of the commutator subgroup, we obtain various criteria characterizing the Riemannian metrics induced by left-invariant purely coclosed G2-structures. Then, we use them to determine the isomorphism classes of 2-step nilpotent Lie algebras admitting such type of structures. As an intermediate step, we show that every metric on a 2-step nilpotent Lie algebra admitting coclosed G2-structures is induced by one of them. Finally, we use our results to give the explicit description of the metrics induced by purely coclosed G2-structures on 2-step nilpotent Lie algebras with derived algebra of dimension at most two, up to automorphism.