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The comment(s) below were originally left at Talk:Lattice (discrete subgroup)/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
Hard to assign a unique field… Arcfrk ( talk) 10:46, 16 February 2008 (UTC) |
Last edited at 10:46, 16 February 2008 (UTC). Substituted at 21:42, 29 April 2016 (UTC)
"Lattices are best thought of as discrete approximations of continuous groups (such as Lie groups)."
This isn't the best viewpoint if your interest is the quotient space.
188.154.206.128 ( talk) 16:15, 21 January 2019 (UTC)
I'm not sure whether discussion of these notions is relevant in the introductory section. As far as i can tell it is equivalent for a discrete subgroup to be either a uniform lattice, quasi-isometric to or coarsely equivalent to its ambient group (with an invariant metric), though i don't know any reference for the latter.
It could make sense to add a section about "lattices in geometric group theory" or something similar where this is discussed. jraimbau ( talk) 12:11, 27 October 2021 (UTC)
In the section Generalities on lattices this sentence appears:
"A lattice is called uniform when the quotient space is compact (and non-uniform otherwise)."
Am I correct to say that, when speaking of a lattice in a Lie group, "cocompact" is a synonym for "uniform"?
If so, then this is worth mentioning in the artice. 2601:200:C000:1A0:C0A2:E29D:72EF:28D2 ( talk) 19:10, 12 May 2022 (UTC)
The section "Rank 1 versus higher rank begins with this sentence:
"The real rank of a Lie group is the maximal dimension of an abelian subgroup containing only semisimple elements.'
The linked article Semisimple does not explain what a "semisimple element" is.
I hope someone knowledgeable about this subject can clarify this. 2601:200:C000:1A0:C0A2:E29D:72EF:28D2 ( talk) 19:20, 12 May 2022 (UTC)