Simple superelliptic Lie algebras

Abstract

Let $m\in N$, $P(t)\in C[t]$. Then we have the Riemann surfaces (commutative algebras) $R_m(P)=C[t^{\pm 1},u|u^m=P(t)]$ and $S_m(P)=C[t,u|u^m=P(t)].$ The Lie algebras ${\mathcal{R}}_m(P)=Der(R_m(P))$ and ${\mathcal{S}}_m(P)=Der(S_m(P))$ are called the $m$-th superelliptic Lie algebras associated to $P(t)$. In this paper we determine the necessary and sufficient conditions for such Lie algebras to be simple, and determine their universal central extensions and their derivation algebras. We also study the isomorphism and automorphism problem for these Lie algebras.

Corrections on Corollaries 15 and 16

References in corpus (3)

• Vertex Algebras and Algebraic Curves
• The Wess-Zumino-Witten-Novikov theory, Knizhnik-Zamolodchikov equations, and Krichever-Novikov algebras, I
• Determining the automorphism group of a hyperelliptic curve

Cited by in corpus (1)

• On the Universal Central Extension of Hyperelliptic Current Algebras