Affordable Access

Similar sublattices of the root lattice A4

Publication Date
  • Mathematics


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.

There are no comments yet on this publication. Be the first to share your thoughts.