  We first examine how T-matrix equivalence drives the flow of similarity
renormalization group (SRG) evolved potential matrix elements to a universal
form, with the ultimate goal of gaining insight into universality for
three-nucleon forces. In agreement with observations made previously for
Lee-Suzuki transformations, regions of universal potential matrix elements are
restricted to where half-on-shell T-matrix equivalence holds, but the
potentials must also reproduce binding energies. We find universality in local
energy regions, reflecting a local decoupling by the SRG. To continue the study
in the 3-body sector, we create a simple 1-D spinless boson "theoretical
laboratory" for a dramatic improvement in computational efficiency. We
introduce a basis-transformation, harmonic oscillator (HO) basis, which is used
for current many-body calculations and discuss the imposed truncations. When
SRG evolving in a HO-basis, we show that the evolved matrix elements, once
transformed back into momentum-representation, differ from those when evolving
with momentum representation. This is because the generator in each basis is
not exactly the same due to the truncation, which creates evolution artifacts
in the 3-body potential matrix elements. In the 2- body sector, this can be
avoided by increasing the basis size, but it remains unclear whether this is
possible in the 3-body sector, as truncation errors in the 3-body sector are
more difficult to avoid, and the computational power required is greatly
increased for three-body evolution.
