In this paper, we study a family of infinite-dimensional Lie algebras X ⠂S, where X stands for the type: A, B, C, D, and S is an abelian group, which generalize the A, B, C, D series of trigonometric Lie algebras. Among the main results, we identify X ⠂S with what are called the covariant algebras of the affine Lie algebra L ⠃S with respect to some automorphism groups, where LS is an explicitly defined associative algebra X ⠂S- viewed as a Lie algebra. We then show that restricted modules of level $ naturally correspond to equivariant quasi...
