logo of Operadia Operadia

Operad: Lie-Yamaguti

abbreviations
LieYamaguti, LY
category
vec
type
symetrique
dimensions

1, 1, 5, 26, 214, 2094, 25458, 360128

properties
generateurs
  • generator c of type s[1,1]
  • generator # of type s[2,1] + s[1,1,1]
relations
  • relation: (xcy)cz+(ycz)cx+(zcx)cy+(x#y#z)+(y#z#x)+(z#x#y)
  • relation: (xcy)#z#u+(ycz)#x#u+(zcx)#y#u
  • equality: x#y#(zcu) = (x#y#z)cu + zc(x#y#u)
  • equality: x#y#(z#u#v) = (x#y#z)#u#v+z#(x#y#u)#v+z#u#(x#y#v)
morphisms
→ , → Lie, → Yam

References