Abstract
For a given gauge invariant state <TEX>$\omega$</TEX> on the CAR algebra A isomorphic with the C<TEX>$\ast$</TEX> -algebra of <TEX>$2{\times}2$</TEX> complex matrices, we construct a family of quantum Markov semigroups on A which leave w invariant. By analyzing their generators, we decompose the algebra A into four eigenspaces of the semigroups and show some properties.
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