Talk:Lattice (group)

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[edit] Self-dual

hey, can someone explain what it means for a lattice to be self-dual? -Lethe

I think the duality theory is what the crystallographers call the reciprocal lattice. Anyway, one can look at it via Pontryagin duality (ie Fourier theory) so that Λ in Rn has a dual lattice Λ* in the dual Rn, which is its annihilator in the natural pairing. The other way is simply to take linear functionals taking integer values on Λ - not much difference except for some factors of 2π.

Charles Matthews 08:25, 17 Jul 2004 (UTC)

[edit] Source of the moved material

The material that I moved here from the lattice disambiguation page appears to have been written by User:Patrick. Michael Hardy 20:03, 4 October 2005 (UTC)

[edit] New To Advanced Math

Hi; I'm trying desperately to understand many of these advanced principals of mathematics, such as lattice groups, but no matter how many times I review the material, it doesn't sink in. Could someone please provide examples, problems to solve (with their solutions) and/or ways to visualize this? beno 26 Jan 2006

Please post at the bottom of talk pages. Anyway, do you know what a group (mathematics) is? If not, you may want to start by getting a book on introductory group theory. I don't know of any I can recommend, unfortunately. linas 16:22, 27 January 2006 (UTC)

I could use a good book on group theory. Problem is, I live in the Dominican Republic and it would cost me almost $100 just to ship the book here! And, after all, the idea of Wikipedia is to BE the book! If the book isn't complete without the examples, do you think you guys could work on some examples for those of us trying to study who have nothing more than the Wikipedia? TIA. beno 31 Jan 2006

First of all, it's not exactly true that the point of wikipedia is to "be the book". We're aiming to write an encyclopedia, not a textbook. So wikipedia isn't necessarily optimal for learning stuff from scratch. In principle, that's what wikibooks is for. In practice, wikibooks is very much less developed than wikipedia. And a lot of wikipedia is quite approachable even if you start from scratch, so your goal isn't entirely unreasonable. That said, some articles are better than others. If some article seems not so readable to you, there are people who'd like to help. If this article isn't "sinking in" for you, maybe we can improve it, so that it will! In order for that to happen, it would be better if you could explain exactly what parts you're not getting. For those of us who know the material already, it can be hard to know exactly where we lose the beginner. Of course, any article is hard if you don't know the prerequisites, so as linas suggests, you should make sure you know what a group is before you tackle lattice groups. So with these points in mind, are there any specific points that I can help you understand? -lethe talk + 15:13, 31 January 2006 (UTC)

[edit] In Lie groups

I have written an article on lattices in Lie groups (and generalizations), which largely eliminates the need for a section on this subject here (modulo redirects). If there are no objections, I will remove this section entirely, it does not fit with the rest of the article. Arcfrk (talk) 09:49, 16 February 2008 (UTC)