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I want to learn about Niemeier lattice and Leech lattice in it. I will be pleased if some one could introduce some books or Lecture notes to me.

flag	asked Apr 17 2011 at 8:15 unknown (yahoo) 53●3

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Have you looked in Conway and Sloane's Sphere Packings, Lattices and Groups? It's a good first reference for just about anything having to do with the objects in the title. Certainly Niemeier and Leech are in there... – Pete L. Clark Apr 17 2011 at 8:56

I need some basics. I have looked at the book but it is a kind of some results about these lattices. Thanks anyways. – unknown (yahoo) Apr 17 2011 at 9:52

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Without knowing more about what you are hoping for, it's hard to give an answer. If you need detailed information about Niemeier lattices, it may be difficult to find sources that are substantially more accessible than Conway and Sloane (although perhaps I am overlooking something). Maybe you would be interested in the book From error-correcting codes through sphere packings to simple groups by Thompson? It doesn't mention Niemeier lattices, but it's a very readable introduction to the Leech lattice, and it is good preparation for Conway and Sloane. – Henry Cohn Apr 17 2011 at 13:06

Jim Humphreys · Accepted Answer · 2011-04-17 21:23:17Z UTC

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The standard reference is Conway and Sloane. If this is too much, you could try Wolfgang Ebeling's book "Lattices and codes A course partially based on lectures by F. Hirzebruch." Advanced Lectures in Mathematics. Friedr. Vieweg & Sohn, Braunschweig, ISBN: 3-528-06497-8. This covers Venkov's classification of Niemeier lattices, and some properties of the Leech lattice

edited Apr 17 2011 at 21:23

Jim Humphreys

answered Apr 17 2011 at 14:26

Richard Borcherds
14.1k●2●54●82

Thanks Henry and Richard. – unknown (yahoo) Apr 17 2011 at 14:43

Oops, I was indeed overlooking something. Ebeling is a good suggestion - it has the advantage of developing things systematically from scratch, while Conway and Sloane is mainly a collection of reprinted papers, with some expository chapters thrown in. If you want to work in this area, eventually you will need to come to terms with Conway and Sloane, but you should think of it as a reference book rather than a textbook. There's an enormous amount of valuable information in it, and some parts are quite accessible, but it was never meant to be read straight through. – Henry Cohn Apr 17 2011 at 15:00

Neat, I'd never heard of Ebeling's book. I have to say that "developing things systematically from scratch" is more to my style than Conway and Sloane's compendious tome of examples and results. (For me it is a very valuable reference, but I can learn only a little bit each time I open it.) I look forward to reading Ebeling. – Pete L. Clark Apr 17 2011 at 18:46

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Note that the AMS distributes Ebeling's book and other Vieweg titles including some English translations. As Henry Cohn comments, the Conway-Sloane volume is better viewed as a reference source. – Jim Humphreys Apr 17 2011 at 21:26

Thanks Jim...You completed the answer...Best – unknown (yahoo) Apr 20 2011 at 13:11

Niemeier Lattice

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