On Supernilpotent Algebras
Abstract
We establish a characterization of supernilpotent Mal'cev algebras which generalizes the affine structure of abelian Mal'cev algebras and the recent characterization of 3-supernilpotent Mal'cev algebras. We then show that for varieties in which the two-generated free algebra is finite: (1) neutrality of the higher commutators is equivalent to congruence meet-semidistributivity, and (2) the class of varieties which interpret a Mal'cev term in every supernilpotent algebra is equivalent to the existence of a weak difference term. We then establish properties of the higher commutator in the aforementioned second class of varieties.
Cite
@article{arxiv.1701.08949,
title = {On Supernilpotent Algebras},
author = {Alexander Wires},
journal= {arXiv preprint arXiv:1701.08949},
year = {2025}
}
Comments
31 pages, corrected typos and formatting, expanded section 5, congruence modular varieties have m-difference terms for all m