Filtration-preserving mappings and centralizers within graded Lie algebras

2009 ◽  
Vol 139 (5) ◽  
pp. 961-996
Author(s):  
M. Bendersky ◽  
G. Chen ◽  
R. C. Churchill
Keyword(s):  
Spectral Sequence ◽  
Lie Algebras ◽  
Normal Forms ◽  
Graded Lie Algebras ◽  
Parameter Matrix ◽  
Sequence Techniques ◽  
Unique Normal Forms ◽  
Finiteness Criterion

We use spectral sequence techniques to compute centralizers of elements within graded Lie algebras, and the methods are then applied to the calculation of unique normal forms of elements within one-parameter matrix Lie algebras. A finiteness criterion for unique normal forms is presented.

Cohomology of certain $ \mathbb N$-graded Lie algebras

2004 ◽  
Vol 59 (6) ◽  
pp. 1210-1211
Author(s):  
D V Millionshchikov ◽  
A Fialowski
Keyword(s):  
Lie Algebras ◽  
Graded Lie Algebras

scholarly journals $\mathbf {Z}/m$-graded Lie algebras and perverse sheaves, IV

2020 ◽  
Vol 24 (12) ◽  
pp. 360-396
Author(s):  
George Lusztig ◽  
Zhiwei Yun
Keyword(s):  
Lie Algebras ◽  
Perverse Sheaves ◽  
Graded Lie Algebras

A SUFFICIENT CONDITION FOR THE UNIQUENESS OF NORMAL FORMS AND UNIQUE NORMAL FORMS OF GENERALIZED HOPF SINGULARITIES

2004 ◽  
Vol 14 (09) ◽  
pp. 3337-3345 ◽  
Author(s):  
JIANPING PENG ◽  
DUO WANG
Keyword(s):  
Normal Form ◽  
Normal Forms ◽  
Sufficient Condition ◽  
First Order ◽  
Recursive Formulas ◽  
Unique Normal Forms

A sufficient condition for the uniqueness of the Nth order normal form is provided. A new grading function is proposed and used to prove the uniqueness of the first-order normal forms of generalized Hopf singularities. Recursive formulas for computation of coefficients of unique normal forms of generalized Hopf singularities are also presented.

Generators of simple graded Lie algebras of finite growth

2017 ◽  
Vol 148 (2) ◽  
pp. 315-324
Author(s):  
Liming Tang ◽  
Wende Liu
Keyword(s):  
Lie Algebras ◽  
Graded Lie Algebras ◽  
Finite Growth
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