Stupid questions raised by rapid perusal of Conway & Sloane (1988): Dimensions 10,12,14,15,16 etc. are not mentioned. What makes these cases harder or less interesting than dimensions 11,13,17,19,23 ? Dimensions 11,19 are included in the early pages; but later sections omit discussion of their lattices. Why is this? Fred Lunnon On 7/28/12, Neil Sloane <njasloane@gmail.com> wrote:
A better reference is
- *146. **Low-Dimensional Lattices II: Subgroups of GL(n, Z)<http://neilsloane.com/doc/Me146.pdf> *, J. H. Conway and N. J. A. Sloane, *Proc. Royal Soc. London, Series A*, 419 (1988), pp. 29-68.
available from my home page (see below), item 146.
On Sat, Jul 28, 2012 at 3:58 PM, Adam P. Goucher <apgoucher@gmx.com> wrote:
I'd recommend reading Sphere Packings, Lattices and Groups, by J. H. Conway and N. J. A. Sloane. That lists all of the known interesting lattices in small numbers of dimensions.
Sincerely,
Adam P. Goucher
Can anyone please point me to any article or book that addresses the
question of what are the maximal finite subgroups of GL(n,Z) ?
What I'm ultimately interested in is this:
Which n-dimensional lattices L (in R^n) have a maximal automorphism group Aut(L) -- maximal as a subgroup of O(n) ?
(Aut(L) here is the group of isometries of R^n that fix the origin and take L onto L.)
E.g., in 2D these are the square and triangular lattices. In 3D I think these are the cubic, bcc and fcc lattices. I don't know the answer for higher dimensions.
Thanks,
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Neil J. A. Sloane, President, OEIS Foundation 11 South Adelaide Avenue, Highland Park, NJ 08904, USA Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun