Normal forms generalizing action-angle coordinates for Hamiltonian actions of Lie groups

1983 ◽  
Vol 7 (1) ◽  
pp. 55-62 ◽  
Author(s):  
Charles-Michel Marle
Keyword(s):  
Lie Groups ◽  
Normal Forms ◽  
Hamiltonian Actions

LEFT INVARIANT COMPLEX STRUCTURES ON NILPOTENT SIMPLY CONNECTED INDECOMPOSABLE 6-DIMENSIONAL REAL LIE GROUPS

2007 ◽  
Vol 17 (01) ◽  
pp. 115-139 ◽  
Author(s):  
L. MAGNIN
Keyword(s):  
Automorphism Group ◽  
Normal Form ◽  
Lie Groups ◽  
Lie Algebras ◽  
Lie Group ◽  
Normal Forms ◽  
Equivalence Classes ◽  
Complex Structures ◽  
Simply Connected ◽  
Connected Lie Group

Integrable complex structures on indecomposable 6-dimensional nilpotent real Lie algebras have been computed in a previous paper, along with normal forms for representatives of the various equivalence classes under the action of the automorphism group. Here we go to the connected simply connected Lie group G0 associated to such a Lie algebra 𝔤. For each normal form J of integrable complex structures on 𝔤, we consider the left invariant complex manifold G = (G0, J) associated to G0 and J. We explicitly compute a global holomorphic chart for G and we write down the multiplication in that chart.

scholarly journals Hamiltonian actions of unipotent groups on compact K\"ahler manifolds

2018 ◽  
Vol Volume 2 ◽  
Author(s):  
Daniel Greb ◽  
Christian Miebach
Keyword(s):  
Lie Groups ◽  
Invariant Theory ◽  
Symplectic Reduction ◽  
Stability Conditions ◽  
Unipotent Group ◽  
Geometric Invariant ◽  
Projective Varieties ◽  
Final Version ◽  
Unipotent Groups ◽  
Hamiltonian Actions

We study meromorphic actions of unipotent complex Lie groups on compact K\"ahler manifolds using moment map techniques. We introduce natural stability conditions and show that sets of semistable points are Zariski-open and admit geometric quotients that carry compactifiable K\"ahler structures obtained by symplectic reduction. The relation of our complex-analytic theory to the work of Doran--Kirwan regarding the Geometric Invariant Theory of unipotent group actions on projective varieties is discussed in detail. Comment: v2: 30 pages, final version as accepted by EPIGA

scholarly journals POINCARÉ NORMAL FORMS AND SIMPLE COMPACT LIE GROUPS

2002 ◽  
Vol 17 (25) ◽  
pp. 3571-3587 ◽  
Author(s):  
GIUSEPPE GAETA
Keyword(s):  
Dynamical Systems ◽  
Lie Groups ◽  
Lie Algebras ◽  
Normal Forms ◽  
Linear Part ◽  
Compact Lie Groups ◽  
Fundamental Representation ◽  
Normalizing Transformations

We classify the possible behavior of Poincaré–Dulac normal forms for dynamical systems in Rn with nonvanishing linear part and which are equivariant under (the fundamental representation of) all the simple compact Lie algebras and thus the corresponding simple compact Lie groups. The "renormalized forms" (in the sense of Ref. 22) of these systems is also discussed; in this way we are able to simplify the classification and moreover to analyze systems with zero linear part. We also briefly discuss the convergence of the normalizing transformations.

METHODS OF REDUCING OF LARGE BOOLEAN FORMULAS REPRESENTED IN A CONJUNCTIVE NORMAL FORM FOR DETERMINING THEIR SATISFIABILITY

2020 ◽  
Author(s):  
N.I. Gdansky ◽  
◽  
A.A. Denisov ◽  
Keyword(s):  
Normal Form ◽  
Normal Forms ◽  
Conjunctive Normal Form ◽  
Boolean Formulas

The article explores the satisfiability of conjunctive normal forms used in modeling systems.The problems of CNF preprocessing are considered.The analysis of particular methods for reducing this formulas, which have polynomial input complexity is given.

Regularization of Integral Operators in Singularly Perturbed Problems Using Normal Forms

Vestnik MEI ◽  
2019 ◽  
Vol 6 ◽  
pp. 131-137
Author(s):  
Abdukhafiz A. Bobodzhanova ◽  
◽  
Valeriy F. Safonov ◽  
Keyword(s):  
Normal Forms ◽  
Integral Operators ◽  
Singularly Perturbed ◽  
Singularly Perturbed Problems
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