The factorial proof for strand endomorphisms

Block permutations and the existing block cycle-trace formula give a CycleTraceTower at every strand arity. The connection-rank bound then forces nilpotent traces to vanish. Nondegeneracy of the connection pairing supplies semisimplicity by the trace criterion. The Schur and trace-zeta proof remains in BlockAssembly.

noncomputable def RS.blockCycleTraceTower {R : ℕ} (f : EdgeRankParameter R) (n : ℕ) : CycleTraceTower (fun (k : ℕ) => skeinEnd f (n * k)) (skeinEnd f n)

The cycle-trace tower at an arbitrary strand arity.

Equations

• One or more equations did not get rendered due to their size.

theorem RS.skeinTrace_eq_zero_of_isNilpotent_factorial {R : ℕ} (f : EdgeRankParameter R) (n : ℕ) {g : skeinEnd f n} (hg : IsNilpotent g) : skeinTrace f n g = 0

The factorial proof of nilpotent-trace vanishing at every strand arity, without a Schur package.

theorem RS.skeinEnd_isSemisimpleRing_factorial {R : ℕ} (f : EdgeRankParameter R) (n : ℕ) : IsSemisimpleRing (skeinEnd f n)

Every strand endomorphism algebra is semisimple by the factorial trace obstruction and the connection pairing.