We find the structure of generators of norm-continuous quantum Markov semigroups on B(h) that are symmetric with respect to the scalar product tr (ρ~(1/2)x*ρ~(1/2)y) induced by a faithful normal invariant state ρ and satisfy two quantum generalisations of the classical detailed balance condition related with this non-commutative notion of symmetry: the so-called standard detailed balance condition and the standard detailed balance condition with an antiunitary time reversal.
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