This is the usual way of introducing majorana operators. First we have $N$ fermionic modes. The corresponding operators satisfy the commutation relations
$$ \{c_i, c_j \}= \{c_i^\dagger, c_j^\dagger \} =0, $$
$$ \{\ c_i , c_j^\dagger \}=\delta_{ij} . $$
Then we introduce the $2N $ majorana operators
$$\gamma_{2j - 1} = c_j + c_j^\dagger, $$
$$ \gamma_{2j} = -i (c_j - c_j^\dagger) . $$
These operators satisfy the conditions
$$ \gamma_l \gamma_m + \gamma_m \gamma_l = 0, \quad l \neq m , $$
$$ \gamma_l \gamma_l = 1 . $$
The question is, can we start directly from these relations and derive the consequence of the algebra? In this way, the number of operators can be odd too.
