We introduce mod 3 triple Milnor invariants and triple cubic residue symbols for certain primes of the Eisenstein number field Q(-3), following the analogies between knots and primes. Our triple symbol generalizes both the cubic residue symbol and Rédei’s triple symbol, and describes the decomposition law of a prime in a mod 3 Heisenberg extension of degree 27 over Q(-3) with restricted ramification, which we construct concretely in the form similar to Rédei’s dihedral extension over Q. We also give a cohomological interpretation of our symbols by triple Massey products in Galois cohomology.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory