Research proof index

Given any short exact sewuence 0 → A → B → C → 0 in Rep R G and any subgroup H of G, the following diagram is commutative Hⁿ(G,C) ⟶ H^{n+1}(G A) | | ↓ ↓ Hⁿ(H,C) ⟶ H^{n+1}(G A). The vertical arrows are restriction and the horizontals are connecting homomorphisms. For this, it would be sensible to define restriction as a natural transformation, so t...

If H²ⁿ⁺²(H,M) and H²ᵐ⁺¹(H,M) are both zero for every subgroup H of G then M is acyclic. -/ theorem groupCohomology.trivialCohomology_of_even_of_odd_of_solvable [Finite G] [Group.IsSolvable G] (M : Rep R G) (n m : ℕ) -- todo: don't quantify over all types (h_even : ∀ (H : Type) [Group H] {φ : H →* G} (_ : Function.Injective φ), IsZero (groupCohom...

If H²ⁿ⁺²(H,M) and H²ᵐ⁺¹(H,M) are both zero for every subgroup H of G then M is acyclic.

Simulating the random oracle leaves the nonzero SRS trapdoor sampler unchanged.

The determinant of an SO(3) matrix minus the identity is equal to zero.

For every element of SO(3) there exists a vector which remains unchanged under the action of that SO(3) element.