Mal'cev's criterion
id:
mal-cev-s-criterion-292-11051312
title:
Mal'cev's criterion
text:
In differential geometry, Mal'cev's criterion, proved by Anatoly Mal'cev, states that a simply connected nilpotent Lie group admits a lattice, i.e., a discrete co-compact subgroup, if and only if the associated Lie algebra admits a basis such that the structure constants are rational. The relevance of Mal'cev's criterion comes from the fact that it gives us a one-to-one correspondence between isomorphism classes of Lie algebras with rational structure constants and compact nilmanifolds. Indeed,
brand slug:
wiki
category slug:
encyclopedia
description:
Theorem for nilmanifolds
original url:
https://en.wikipedia.org/wiki/Mal%27cev%27s_criterion
date created:
date modified:
2023-11-27T18:34:10Z
main entity:
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image:
fields total:
13
integrity:
14