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Operad: Gerstenhaber

abbreviation
Gerst
category
dgvec
type
symetrique
dimensions

1, 1-t, 2*t^2 - 3*t + 1, -6*t^3 + 11*t^2 - 6*t + 1

Formula: prod(1 - k*t for k in range(1,n))

Actions: s[1], (-t+1)*s[2], (t^2-t)*s[2, 1] + (-t+1)*s[3], (-t^3+t^2)*s[2, 1, 1] + (t^2-t)*s[2, 2] + (-t^3+2*t^2-t)*s[3, 1] + (-t+1)*s[4], (t^4-t^3)*s[2, 1, 1, 1] + (t^4-2*t^3+t^2)*s[2, 2, 1] + (t^4-3*t^3+2*t^2)*s[3, 1, 1] + (t^4-2*t^3+2*t^2-t)*s[3, 2] + (t^4-2*t^3+2*t^2-t)*s[4, 1] + (-t+1)*s[5], (-t^5+t^4)*s[2, 1, 1, 1, 1] + (-t^5+3*t^4-2*t^3)*s[2, 2, 1, 1] + (-t^5+2*t^4-t^3)*s[2, 2, 2] + (-2*t^5+4*t^4-2*t^3)*s[3, 1, 1, 1] + (-3*t^5+6*t^4-5*t^3+2*t^2)*s[3, 2, 1] + (2*t^4-3*t^3+t^2)*s[3, 3] + (-t^5+4*t^4-5*t^3+2*t^2)*s[4, 1, 1] + (-2*t^5+4*t^4-3*t^3+2*t^2-t)*s[4, 2] + (-t^5+2*t^4-2*t^3+2*t^2-t)*s[5, 1] + (-t+1)*s[6]

properties
Koszul, binary, quadratic, Hopf
Koszul dual operad
Gerst
generateurs
  • generator * of type s[2] of degree 0
  • generator c of type s[2] of degree 1
morphisms
BV, → Com

References