scholarly journals Actions of solvable Lie algebras on rings with no nilpotent elements

1990 ◽  
Vol 135 (1) ◽  
pp. 217-227 ◽  
Author(s):  
Jeffrey Bergen
Keyword(s):  
Lie Algebras ◽  
Nilpotent Elements ◽  
Solvable 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

On Weight Systems Derived from Heisenberg Lie Algebras

2003 ◽  
Vol 12 (05) ◽  
pp. 589-604
Author(s):  
Hideaki Nishihara
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Weight System ◽  
Infinite Dimensional ◽  
Conway Polynomial ◽  
Knot Invariant ◽  
Polynomial Representations ◽  
Solvable Lie Algebras

Weight systems are constructed with solvable Lie algebras and their infinite dimensional representations. With a Heisenberg Lie algebra and its polynomial representations, the derived weight system vanishes on Jacobi diagrams with positive loop-degree on a circle, and it is proved that the derived knot invariant is the inverse of the Alexander-Conway polynomial.

scholarly journals Indecomposable modules of a family of solvable Lie algebras

2017 ◽  
Vol 531 ◽  
pp. 423-446 ◽  
Author(s):  
Paolo Casati ◽  
Andrea Previtali ◽  
Fernando Szechtman
Keyword(s):  
Lie Algebras ◽  
Indecomposable Modules ◽  
Solvable Lie Algebras
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