The 't Hooft η symbol is a symbol which allows one to express the generators of the SU(2) Lie algebra in terms of the generators of Lorentz algebra. The symbol is a blend between the Kronecker delta and the Levi-Civita symbol. It was introduced by Gerard 't Hooft. It is used in the construction of the BPST instanton. ηaμν is the 't Hooft symbol: In other words, they are defined by where the latter are the anti-self-dual 't Hooft symbols. More explicitly, these symbols are and They satisfy the self-duality and the anti-self-duality properties: Some other properties are The same holds for except for