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NCTS Seminar on Complex Geometry
 
10:30 - 11:30, May 27, 2019 (Monday)
R440, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 440室)
Variation of Complex Structures and Variation of Lie Algebras
Stephen S. T. Yau (Tsinghua University)

Abstract:

The classification of nilpotent Lie algebras in higher dimensions (n > 7) remains to be open. There are one-parameter families of non-isomorphic nilpotent Lie algebras (but no two-parameter families) in dimension seven. Dimension seven is the watershed of the existence of such families. It is well-known that no such family exists in dimension n < 7, while it is hard to construct one-parameter family in dimension n > 7. We construct an one-parameter family of solvable (resp. nilpotent) Lie algebras of dimension 11 (resp. 10) from singularities and show that the weak Torelli-type theorem holds. We shall also construct an one-parameter family of solvable (resp. nilpotent) Lie algebras of dimension 12 (resp. 11) from  singularities and show that the Torelli-type theorem holds.
 
Joint work with B.-Y. Chen, N. Hussain and H.-Q. Zuo.


 

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