In 2000, K. Saito and D. Yoshii gave a Serre-type theorem for the simply-laced elliptic Lie algebras. We extend the theorem to that for the elliptic Lie algebras associated with the (reduced marked) elliptic root systems with rank ≥ 2.
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Hiroyuki Yamane, A Serre-type Theorem for the Elliptic Lie Algebras with Rank ≥ 2. Publ. Res. Inst. Math. Sci. 40 (2004), no. 2, pp. 441–469DOI 10.2977/PRIMS/1145475810