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Unitary transformations of a Hamiltonian generally induce interaction termsbeyond the particle rank present in the untransformed Hamiltonian that have tobe captured and included in a many-body calculation. In systems withstrangeness such as hypernuclei, the three-body terms induced by thehyperon-nucleon interaction are strong, so their inclusion is crucial. Wepresent in detail a procedure for computing hyperon-nucleon-nucleon interactionterms that are induced during a similarity renormalization group (SRG) flow.The SRG is carried out in a basis spanned by antisymmetric harmonic-oscillatorstates with respect to three-body Jacobi coordinates. We discuss basisconstruction, antisymmetrization, numerical evaluation of the flow equations,and separation of the genuine three-body terms. We then use the hypernuclearno-core shell model with SRG-evolved Hamiltonians, addressing the sensitivityof hypernuclear states and hyperon separation energies to changes in thenucleonic Hamiltonian by example of $^7_\Lambda$Li, $^9_\Lambda$Be,$^{11}_\Lambda$B, $^{13}_\Lambda$C, and the hyper-helium chain. We also presenta survey of the hyper-hydrogen chain, exploring the structure of hypernucleiwith extreme neutron-proton asymmetries.

Similarity renormalization group evolution of hypernuclear Hamiltonians