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.

Lie Groups, Lie Algebras, Cohomology and some Applications in Physics

1995 ◽  
Author(s):  
Josi A. de Azcárraga ◽  
Josi M. Izquierdo
Keyword(s):  
Lie Groups ◽  
Lie Algebras

The rigidity of some solvable Lie algebras

2018 ◽  
Vol 2018 (2) ◽  
pp. 43-49
Author(s):  
R.K. Gaybullaev ◽  
Kh.A. Khalkulova ◽  
J.Q. Adashev
Keyword(s):  
Lie Algebras ◽  
Solvable Lie Algebras

Optimization of Geometric Structures of New Materials on Parallel Computers

1998 ◽  
Author(s):  
John H. Weare ◽  
Ryoichi Kawai ◽  
Beth Ong
Keyword(s):  
Parallel Computers ◽  
New Materials ◽  
Geometric Structures

Integrable two-dimensional dynamical systems and the characteristic Lie algebras

2007 ◽  
Vol 5 ◽  
pp. 195-200
Author(s):  
A.V. Zhiber ◽  
O.S. Kostrigina
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Second Order ◽  
System Of Equations ◽  
Two Dimensional ◽  
Finite Dimensional ◽  
Dimensional Dynamical System

In the paper it is shown that the two-dimensional dynamical system of equations is Darboux integrable if and only if its characteristic Lie algebra is finite-dimensional. The class of systems having a full set of fist and second order integrals is described.

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