Simple superelliptic Lie algebras
Ben Cox, Xiangqian Guo, Rencai Lu, Kaiming Zhao

TL;DR
This paper investigates the structure of superelliptic Lie algebras derived from specific algebraic curves, providing criteria for their simplicity, and exploring their central extensions, derivations, and automorphisms.
Contribution
It offers the first comprehensive criteria for simplicity and characterizes universal central extensions and automorphisms of superelliptic Lie algebras.
Findings
Criteria for simplicity of superelliptic Lie algebras
Explicit descriptions of universal central extensions
Classification of automorphisms and isomorphisms
Abstract
Let , . Then we have the Riemann surfaces (commutative algebras) and The Lie algebras and are called the -th superelliptic Lie algebras associated to . 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.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Nonlinear Waves and Solitons
