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We find the structure of generators of norm continuous quantum Markovsemigroups on B(h) that are symmetric with respect to the scalar producttr(\rho^{1/2}x\rho^{1/2}y) induced by a faithful normal invariant stateinvariant state \rho and satisfy two quantum generalisations of the classicaldetailed balance condition related with this non-commutative notion ofsymmetry: the so-called standard detailed balance condition and the standarddetailed balance condition with an antiunitary time reversal.

Generators of KMS Symmetric Markov Semigroups on B(h) Symmetry and Quantum Detailed Balance