Operad: Lie

abbreviation

Lie

category

vec

type

symetrique

dimensions

1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880

OEIS: A000142

Formula: factorial(n - 1)

Serie: -log(1 - x)

Equation: (1-x)*diff(P,x)-1

Actions: s[1], s[1, 1], s[2, 1], s[2, 1, 1] + s[3, 1], s[2, 1, 1, 1] + s[2, 2, 1] + s[3, 1, 1] + s[3, 2] + s[4, 1], s[2, 1, 1, 1, 1] + 2*s[2, 2, 1, 1] + s[3, 1, 1, 1] + 3*s[3, 2, 1] + s[3, 3] + 2*s[4, 1, 1] + s[4, 2] + s[5, 1]

properties

Koszul, binary, quadratic, cyclic, NielsenSchreier

Koszul dual operad

Com

generateurs

• generator c of type s[1, 1]

relations

• relation: (xcy)cz+(ycz)cx+(zcx)cy

morphisms

↣ As, ↣ PreLie, ↣ LieAdm, ↣ Pois, → Λ, ↠ MetabelianLie

References

• Folklore