Journal of the
Korean Mathematical Society JKMS

In this paper we shall explicitly calculate the formula of the algebraic presentation of an embedding of the Teichm\"uller space $\mathfrak{T}(M)$ into the Goldman space $\mathcal{G}(M)$. From this algebraic presentation, we shall show that the Goldman's length parameter on $\mathcal{G}(M)$ is an isometric extension of the Fenchel-Nielsen's length parameter on $\mathfrak{T}(M).$

Keywords: convex real projective structure, Hilbert metric, Teichm\"uller space, Goldman space, length parameter.

MSC numbers: 58D27, 53D30