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Similar sublattices of the root lattice $A_4$ by Baake, Michael; Heuer, Manuela; Moody, Robert V. is a scholarly article available to read on EtoBox.

What is Similar sublattices of the root lattice $A_4$ about?

Similar sublattices of the root lattice $A_4$ are possible, according to a result of Conway, Rains and Sloane, for each index that is the square of a non-zero integer of the form $m^2 + mn - n^2$. Here, we add a constructive approach, based on the arithmetic of the quaternion algebra $\mathbb{H} (\mathbb{Q} (\sqrt{5}))$ 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.

Author

Baake, Michael; Heuer, Manuela; Moody, Robert V.

Published

2007

Language

EN