Lie G-Tori of Symplectic Type

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We classify centerless Lie G-tori of type Cᵣ 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 C₂ 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 Cᵣ by Allison and Gao.