Finite Dimensional Lie Algebras in Singularities

José Luis Cisneros Molina () and Meral Tosun ()
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José Luis Cisneros Molina: Universidad Nacional Autónoma de México, Unidad Cuernavaca, Instituto de Matemáticas
Meral Tosun: Galatasaray University, Çirağan Caddesi

Chapter Chapter 10 in Handbook of Geometry and Topology of Singularities I, 2020, pp 541-587 from Springer

Abstract: Abstract Complex simple Lie algebras with simply laced root systems are classified by Dynkin diagrams of type An, Dn, E6, E7, and E8. Also the dual graphs of the minimal resolution of Kleinian singularities are precisely the same aforementioned Dynkin diagrams. In this work, we recall the basic definitions and some results of the theory of complex Lie algebras and of Kleinian singularities, in order to present a relation between finite dimensional complex simple Lie algebras and the Kleinian singularities, given by a theorem by Brieskorn. We also present the extension of Brieskorn’s theorem to the simple elliptic singularity D ~ 5 $$\tilde {D}_5$$ .

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-53061-7_10

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DOI: 10.1007/978-3-030-53061-7_10

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