MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.

share|cite|improve this question
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 '11 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. – user13684 Apr 17 '11 at 9:52
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 '11 at 13:06
up vote 7 down vote accepted

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

share|cite|improve this answer
Thanks Henry and Richard. – user13684 Apr 17 '11 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 '11 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 '11 at 18:46
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 '11 at 21:26
Thanks Jim...You completed the answer...Best – user13684 Apr 20 '11 at 13:11

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.