Nilpotent algebras, implicit function theorem, and polynomial quasigroups
Rings and Algebras
2022-08-23 v1 Group Theory
Abstract
We study finite-dimensional nonassociative algebras. We prove the implicit function theorem for such algebras. This allows us to establish a correspondence between such algebras and quasigroups, in the spirit of classical correspondence between divisible torsion-free nilpotent groups and rational nilpotent Lie algebras. We study the related questions of the commensurators of nilpotent groups, filiform Lie algebras of maximal solvability length and partially ordered algebras.
Cite
@article{arxiv.2208.09527,
title = {Nilpotent algebras, implicit function theorem, and polynomial quasigroups},
author = {Yuri Bahturin and Alexander Olshanskii},
journal= {arXiv preprint arXiv:2208.09527},
year = {2022}
}