Lie G-Tori of Symplectic Type

We classify centerless Lie G-tori of type C_r including the most difficult case r=2 by applying techniques due to Seligman. In particular, we show that the coordinate algebra of a Lie G-torus of type C_2 is either an associative G-torus with involution or a Clifford G-torus. Our results generalize the classification of the core of the extended affine Lie algebras of type C_r by Allison and Gao.