On the existence of derivations as square roots of generators of state-symmetric quantum Markov semigroups

Cipriani and Sauvageot have shown that for any [Formula: see text]-generator text] of a tracially symmetric quantum Markov semigroup on C*-algebra there exists densely defined derivation from to Hilbert bimodule such text]. Here, we show this construction can in general not be generalized semigroups are with respect non-tracial state. In particular, all derivations bimodules assumed concrete form, then use form the finite-dimensional case existence is equivalent positive matrix solution system linear equations. We solve equations examples using Mathematica complete proof.