Parallelisms, prolongations of Lie algebras and rigid geometric structures

2004 ◽  
Vol 114 (3) ◽  
Author(s):  
Alberto Candel ◽  
Raul Quiroga-Barranco
Keyword(s):  
Lie Algebras ◽  
Geometric Structures ◽  
Rigid Geometric Structures

scholarly journals Geometric structures on Lie algebras and double extensions

2018 ◽  
Vol 146 (10) ◽  
pp. 4199-4209 ◽  
Author(s):  
M. C. Rodríguez-Vallarte ◽  
G. Salgado
Keyword(s):  
Lie Algebras ◽  
Geometric Structures

scholarly journals Generalized punctual Hilbert schemes and 𝔤-complex structures

2021 ◽  
Author(s):  
Alexander Thomas
Keyword(s):  
Lie Algebras ◽  
Moduli Spaces ◽  
Hilbert Scheme ◽  
Complex Structure ◽  
Complex Structures ◽  
Hilbert Schemes ◽  
Simple Complex ◽  
Geometric Structures ◽  
Punctual Hilbert Scheme ◽  
Alternative Description

We define and analyze various generalizations of the punctual Hilbert scheme of the plane, associated to complex or real Lie algebras. Out of these, we construct new geometric structures on surfaces whose moduli spaces share multiple properties with Hitchin components, and which are conjecturally homeomorphic to them. For simple complex Lie algebras, this generalizes the higher complex structure. For real Lie algebras, this should give an alternative description of the Hitchin–Kostant–Rallis section.

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