Lie algebras graded by the weight system (Θ ,sl)

On Weight Systems Derived from Heisenberg Lie Algebras

Journal of Knot Theory and Its Ramifications ◽

10.1142/s0218216503002640 ◽

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.

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VASSILIEV KNOT INVARIANTS COMING FROM LIE ALGEBRAS AND 4-INVARIANTS

Journal of Knot Theory and Its Ramifications ◽

10.1142/s0218216501000809 ◽

2001 ◽

Vol 10 (01) ◽

pp. 161-169 ◽

Cited By ~ 22

Author(s):

E. SOBOLEVA

Keyword(s):

Lie Algebra ◽

Lie Algebras ◽

Finite Order ◽

Adjacency Matrix ◽

Weight System ◽

Knot Invariants ◽

The Relationship

We study the 4-bialgebra of graphs and the bialgebra of 4-invariants introduced by S. K. Lando. Our main goal is the investigation of the relationship between 4-invariants of graphs and weight systems arising in the theory of finite order invariants of knots. In particular, we show that the corank of the adjacency matrix of a graph leads to the weight system coming from the defining representation of the Lie algebra gl(N).

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

10.1017/cbo9780511599897 ◽

1995 ◽

Cited By ~ 90

Author(s):

Josi A. de Azcárraga ◽

Josi M. Izquierdo

Keyword(s):

Lie Groups ◽

Lie Algebras

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The rigidity of some solvable Lie algebras

Uzbek Mathematical Journal ◽

10.29229/uzmj.2018-2-4 ◽

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

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Integrable two-dimensional dynamical systems and the characteristic Lie algebras

Proceedings of the Mavlyutov Institute of Mechanics ◽

10.21662/uim2007.1.023 ◽

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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Reduction of partially invariant submodels of rank 3 defect 1 to invariant submodels

Multiphase Systems ◽

10.21662/mfs2018.3.009 ◽

2018 ◽

Vol 13 (3) ◽

pp. 59-63 ◽

Cited By ~ 1

Author(s):

D.T. Siraeva

Keyword(s):

Equation Of State ◽

Lie Algebra ◽

Lie Algebras ◽

Gas Dynamics ◽

Hydrodynamic Type ◽

System Of Equations ◽

Two Dimensional ◽

Equations Of Gas Dynamics ◽

Entropy Functions

Equations of hydrodynamic type with the equation of state in the form of pressure separated into a sum of density and entropy functions are considered. Such a system of equations admits a twelve-dimensional Lie algebra. In the case of the equation of state of the general form, the equations of gas dynamics admit an eleven-dimensional Lie algebra. For both Lie algebras the optimal systems of non-similar subalgebras are constructed. In this paper two partially invariant submodels of rank 3 defect 1 are constructed for two-dimensional subalgebras of the twelve-dimensional Lie algebra. The reduction of the constructed submodels to invariant submodels of eleven-dimensional and twelve-dimensional Lie algebras is proved.

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