Note on nilpotent and solvable algebras

1955 ◽  
Vol 51 (1) ◽  
pp. 37-40 ◽  
Author(s):  
E. M. Patterson
Keyword(s):  
Lie Algebras ◽  
Linear Algebra ◽  
Derived Length ◽  
Solvable Lie Algebras

In general, the class of a nilpotent linear algebra of dimension n is at most n + 1, and the index, or derived length, of a solvable linear algebra of dimension n is at most n. In this note it is shown that, for a nilpotent linear algebra of dimension n satisfying x2 = 0 for all x, the class is at most n; and bounds are obtained for the indices of solvable Lie algebras.

On the derived length of solvable Lie algebras

1988 ◽  
Vol 282 (3) ◽  
pp. 503-511 ◽  
Author(s):  
Rolf Farnsteiner ◽  
Helmut Strade
Keyword(s):  
Lie Algebras ◽  
Derived Length ◽  
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

scholarly journals Classification of Symmetry Lie Algebras of the Canonical Geodesic Equations of Five-Dimensional Solvable Lie Algebras

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1354 ◽  
Author(s):  
Hassan Almusawa ◽  
Ryad Ghanam ◽  
Gerard Thompson
Keyword(s):  
Lie Groups ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Vector Fields ◽  
Solvable Lie Groups ◽  
Related System ◽  
Geodesic Equations ◽  
Solvable Lie Algebras ◽  
Symmetry Algebras

In this investigation, we present symmetry algebras of the canonical geodesic equations of the indecomposable solvable Lie groups of dimension five, confined to algebras A 5 , 7 a b c to A 18 a . For each algebra, the related system of geodesics is provided. Moreover, a basis for the associated Lie algebra of the symmetry vector fields, as well as the corresponding nonzero brackets, are constructed and categorized.

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