Baake, Michael; Heuer, Manuela and Moody, Robert V.
Similar sublattices of the root lattice A4.
Journal of Algebra, 320(4) pp. 1391–1408.
Similar sublattices of the root lattice A4 are possible [J.H. Conway, E.M. Rains, N.J.A. Sloane, On the existence of similar sublattices, Can. J. Math. 51 (1999) 1300–1306] for each index that is the square of a non-zero integer of the form m2+mn−n2. Here, we add a constructive approach, based on the arithmetic of the quaternion algebra H(Q(√5)) and the existence of a particular involution of the second kind, which also provides the actual sublattices and the number of different solutions for a given index. The corresponding Dirichlet series generating function is closely related to the zeta function of the icosian ring.
||2008 Michael Baake
|Project Funding Details:
|Funded Project Name||Project ID||Funding Body|
|Combinatorics of Sequences and Tilings and its Applications||EP/D058465/1||EPSRC|
||similar sublattices; icosian ring; zeta function
||Mathematics, Computing and Technology > Mathematics and Statistics
||19 Jan 2009 08:21
||21 Mar 2014 12:00
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