In this paper, we introduce the concept of operator-valued quadratic form based on Hilbert W*-module \documentclass[12pt]{minimal}
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\begin{document}$l_2 \bar \otimes A$\end{document}, and give a one to one correspondence between the set of positive self-adjoint regular module operators on \documentclass[12pt]{minimal}
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\begin{document}$l_2 \bar \otimes A$\end{document} and the set of regular quadratic forms, where A is a finite and σ-finite von Neumann algebra. Furthermore, we obtain that a strict continuous symmetric regular module operator semigroup \documentclass[12pt]{minimal}
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\begin{document}$\{ T_t \} _{t \in \mathbb{R}^ + } \subset L(l_2 \bar \otimes A)$\end{document} is Markovian if and only if the associated A-valued quadratic form is a Dirichlet form, where L(\documentclass[12pt]{minimal}
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\begin{document}$l_2 \bar \otimes A$\end{document}) is the von Neumann algebra of all adjointable module maps on \documentclass[12pt]{minimal}
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\begin{document}$l_2 \bar \otimes A$\end{document}.
