Notices of the International Consortium of Chinese Mathematicians

Volume 10 (2022)

Number 2

On derivation Lie algebras of singularities and Torelli-type theorems

Pages: 30 – 39

DOI: https://dx.doi.org/10.4310/ICCM.2022.v10.n2.a3

Authors

Stephen S.-T. Yau (Department of Mathematical Sciences, Tsinghua University, Beijing, China; and Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, Huairou, China)

Huaiqing Zuo (Department of Mathematical Sciences, Tsinghua University, Beijing, China)

Abstract

Since Brieskorn gave the connection between simple Lie algebras and ADE singularities in 1970, it has become an important problem to establish connections between singularities and solvable (nilpotent) Lie algebras. Recently, we have constructed some new natural maps between the set of complex analytic isolated singularities and the set of finite dimensional solvable (nilpotent) Lie algebras. Furthermore, we use these new Lie algebras to obtain Torelli-type theorems of simple elliptic singularities. The main purpose of this paper is to summarize the results that we have obtained on new Lie algebras arising from isolated hypersurface singularities.

Keywords

derivation, Lie algebra, isolated singularity

2010 Mathematics Subject Classification

14B05, 32S05

Full Text (PDF format)

Both Yau and Zuo were supported by NSFC Grant 11961141005. Zuo was supported by NSFC Grant 12271280 and Tsinghua University Initiative Scientific Research Program. Yau was supported by Tsinghua University Education Foundation fund (042202008).

Published 6 February 2023