I am learning Hyperbolic Geometry. Few days ago I attended a seminar on hyperbolic geometry.
The professor introduced us with Teichmüller space and later he presented Teichmüller space is as a representation space for surface groups into $\text{PSL}(2,\mathbb{R})$ (the group is known as the isometry group of the Poincare half-plane model of the hyperbolic plane). Later, he told that a natural generalization is to consider surface group representations in other semisimple Lie groups.
My question is as follows: Is $\text{PSL}(2,\mathbb{R})$ a semisimple Lie group?