Operad: Di-alternative

abbreviation

DiAlt

category

vec

type

symetrique

dimensions

1, 4, 21, 72, 360

properties

binary, quadratic, non-Koszul

generateurs

• generator ⊣ of type s[1]**2
• generator ⊢ of type s[1]**2

relations

• equality: (x⊣y)⊣z - x⊣(y⊣z) = -(z⊢y)⊢x + z⊢(y⊢x)
• equality: (x⊣y)⊣z - x⊣(y⊣z) = (y⊢z)⊢x - y⊢(z⊢x)
• equality: (x⊢y)⊣z - x⊢(y⊣z) = -(x⊢z)⊢y + x⊢(z⊢y)
• equality: (x⊣y)⊢z = x⊢(y⊢z)
• equality: (x⊣y)⊣z = x⊣(y⊢z)

References

• Dong Liu, 2005 ↗