On central extensions and simply laced Lie algebras

Beth Romano

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arXiv · 1912.10254

On central extensions and simply laced Lie algebras

Beth Romano

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Abstract

Let $Λ$ be a simply laced root lattice and $w$ an elliptic automorphism of $Λ$ of order $d$. This paper gives a construction that begins with a central extension of the group of coinvariants $Λ_w$ and produces a semisimple Lie algebra of Dykin type $Λ$ with an automorphism of order $d$ lifting $w$. The input for this construction naturally arises when considering certain families of algebraic curves. The construction generalizes one used by Thorne to study plane quartics and one used by the author and Thorne to study a family of genus-2 curves.

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Beth Romano. 2020-11-03. On central extensions and simply laced Lie algebras. https://arxiv.org/abs/1912.10254

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