  We present the first ab initio calculations for $p$-shell hypernuclei
including hyperon-nucleon-nucleon (YNN) contributions induced by a Similarity
Renormalization Group transformation of the initial hyperon-nucleon
interaction. The transformation including the YNN terms conserves the spectrum
of the Hamiltonian while drastically improving model-space convergence of the
Importance-Truncated No-Core Shell Model, allowing a precise extraction of
binding and excitation energies. Results using a hyperon-nucleon interaction at
leading order in chiral effective field theory for lower- to mid-$p$-shell
hypernuclei show a good reproduction of experimental excitation energies while
hyperon binding energies are typically overestimated. The induced YNN
contributions are strongly repulsive and we show that they are related to a
decoupling of the $\Sigma$ hyperons from the hypernuclear system, i.e., a
suppression of the $\Lambda$-$\Sigma$ conversion terms in the Hamiltonian. This
is linked to the so-called hyperon puzzle in neutron-star physics and provides
a basic mechanism for the explanation of strong $\Lambda$NN three-baryon
forces.
