×

zbMATH — the first resource for mathematics

Even unimodular Gaussian lattices of rank 12. (English) Zbl 1075.11048
Summary: We classify even unimodular Gaussian lattices of rank 12, that is, even unimodular integral lattices of rank 12 over the ring of Gaussian integers. This is equivalent to the classification of the automorphisms \(\tau \) with \(\tau ^2 = -1 \) in the automorphism groups of all the Niemeier lattices, which are even unimodular (real) integral lattices of rank 24. There are 28 even unimodular Gaussian lattices of rank 12 up to equivalence.

MSC:
11H06 Lattices and convex bodies (number-theoretic aspects)
11H56 Automorphism groups of lattices
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Buser, P.; Sarnak, P., On the period matrix of a Riemann surface of large genus, with an appendix by J. H. Conway and N. J. A. sloane, Invent. math., 117, 27-56, (1994) · Zbl 0814.14033
[2] Conway, J.H.; Curtis, R.T.; Norton, S.P.; Parker, R.A.; Wilson, R.A., Atlas of finite groups, (1985), Clarendon Press Oxford · Zbl 0568.20001
[3] Conway, J.H.; Sloane, N.J.A., Sphere packing, lattices and groups, (1999), Springer-Verlag New York · Zbl 0915.52003
[4] Hashimoto, K.; Sibner, R.J., Involutive modular transformations on the Siegel upper half plane and an application to representations of quadratic forms, J. number theory, 23, 102-110, (1986) · Zbl 0585.10017
[5] Iyanaga, K., Class numbers of definite Hermitian forms, J. math. soc. Japan, 21, 359-374, (1969) · Zbl 0182.07101
[6] Niemeier, H.-V., Definete quadratische formen der dimension 24 und diskriminante 1, J. number theory, 5, 142-178, (1973) · Zbl 0258.10009
[7] Venkov, B.B., Even unimodular 24-dimensional lattices, (), 429-440
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.