  We study the Lorentz and Dirac algebra, including antisymmetric $\epsilon$
tensors and the $\gamma_5$ matrix, in implicit gauge-invariant
regularization/renormalization methods defined in fixed integer dimensions.
They include constrained differential, implicit and four-dimensional
renormalization. We find that these fixed-dimension methods face the same
difficulties as the different versions of dimensional regularization. We
propose a consistent procedure in these methods, similar to the consistent
version of regularization by dimensional reduction.
