Similar Sublattices of the Root Lattice a 4
نویسنده
چکیده
Similar sublattices of the root lattice A4 are possible [9] for each index that is the square of a non-zero integer of the form m + mn − n. 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.
منابع مشابه
Similar Sublattices and Coincidence Rotations of the Root Lattice A4 and Its Dual
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