We prove that the invariance of the N=2 superconformal quantum mechanics is
controlled by subalgebras of a given twisted superalgebra made of 6 fermionic
(nilpotent) generators and 6 bosonic generators (including a central charge).
The superconformal quantum mechanics actions are invariant under this quite
large twisted superalgebra. On the other hand, they are fully determined by a
subalgebra with only 2 fermionic and 2 bosonic (the central charge and the
ghost number) generators. The invariant actions are Q_i-exact (i=1,2,...,6),
with a Q_{i'}-exact (i'\neq i) antecedent for all 6 fermionic generators. It
follows that the superconformal quantum mechanics actions with Calogero
potentials are uniquely determined even if, in its bosonic sector, the twisted
superalgebra does not contain the one-dimensional conformal algebra sl(2), but
only its Borel subalgebra. The general coordinate covariance of the non-linear
sigma-model for the N=2 supersymmetric quantum mechanics in a curved target
space is fully implied only by its worldline invariance under a pair of the 6
twisted supersymmetries. The transformation connecting the ordinary and twisted
formulations of the N=2 superconformal quantum mechanics is explicitly
presented.Comment: Minor corrections in some formula
