We extend the construction of Dirichlet forms and symmetric Markovian semigroups on standard forms of von Neumann algebras given in  to the case of ℤ2-graded von Neumann algebras. As an application of the extension, we construct symmetric Markovian semigroups on CAR algebras with respect to gauge invariant quasi-free states and also investigate detailed properties such as ergodicity of the semigroups.
Bibliographical noteFunding Information:
This work was supported by Korea Research Foundation Grant (KRF-2001-005-D20003). The authors wish to thank anonymous referees for suggesting several improvements.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics