• Corpus ID: 13959353

Nonabelian Toda equations associated with classical Lie groups

@article{Razumov1999NonabelianTE,
  title={Nonabelian Toda equations associated with classical Lie groups},
  author={A. V. Razumov and Mikhail V. Saveliev and A. Zuevsky},
  journal={arXiv: Mathematical Physics},
  year={1999}
}
The grading operators for all nonequivalent Z-gradations of classical Lie algebras are represented in the explicit block matrix form. The explicit form of the corresponding nonabelian Toda equations is given. 
View PDF on arXiv
13 Citations
Highly Influential Citations
2
Background Citations
5
Methods Citations
5

13 Citations

Toda equations associated with loop groups of complex classical Lie groups

ℤ-graded loop Lie algebras, loop groups, and Toda equations

We consider Toda equations associated with twisted loop groups. Such equations are specified by ℤ-gradings of the corresponding twisted loop Lie algebras. We discuss the classification of Toda…

Modified non-Abelian Toda field equations and twisted quasigraded Lie algebras

We construct a new family of quasigraded Lie algebras that admit the Kostant-Adler scheme. They coincide with special quasigraded deformations of twisted subalgebras of the loop algebras. Using them…

W-algebras for non-abelian Toda systems

Higher Symmetries of Toda Equations

The symmetries of the simplest non-abelian Toda equations are discussed. The set of characteristic integrals whose Hamiltonian counterparts form a W-algebra, is presented.

Generalized Calogero system for simple Lie algebra series

We derive equations of motions and solutions for the generalized spin-Calogero models associated for the classical Lie algebra series Bn, Cn BCn, and Dn using the pole expansion.

On classification of non-abelian Toda systems

A simple procedure to enumerate all Toda systems associated with complex classical Lie groups is given.

Non-Commutative Ricci and Calabi Flows

Abstract.Starting from an improved version of the bicomplex structure associated the continual Lie algebra with non-commutative base algebra, we obtain dynamical systems resulting from the bicomplex…

O ct 2 00 2 W-algebras for non-abelian Toda systems

We construct the classical W -algebras for some non-abelian Toda systems associated with the Lie groups GL 2n(R) and Spn(R). We start with the set of characteristic integrals and find the Poisson…

Quantum group perturbative formalism for affine Toda models

In the case of non-compact space we consider the quantum affine Toda systems in the operator approach. We introduce quantum analogues of the systems of equations as well as elements of quantum…

References

SHOWING 1-10 OF 13 REFERENCES

Factorization of differential operators, quasideterminants, and nonabelian Toda field equations

We integrate nonabelian Toda field equations for root systems of types A, B, C, for functions with values in any associative algebra. The solution is expressed via quasideterminants. In the appendix…

Maximally non-abelian Toda systems☆

Lie algebras, geometry and Toda-type systems

Preface 1. Introductory data on Lie algebras 2. Basic notions of differential geometry 3. Differential geometry of Toda type systems 4. Toda type systems and their explicit solutions References…

Two-dimensional Ultra-Toda integrable mappings and chains (Abelian case)

The new class of integrable mappings and chains is introduced. Corresponding (1+2) integrable systems invariant with respect to such discrete transformations are represented in explicit form. Soliton…

Multi-dimensional toda-type systems

A wide class of multi-dimensional nonlinear systems of partial differential equations is obtained and an integration scheme for such equations is proposed.

Higher grading generalisations of the Toda systems

Graded Lie algebras, representation theory, integrable mappings and systems

The exactly integrable systems connected with semisimple algebras of the second rank $A_2,B_2,C_2,G_2$

All exactly integrable systems connected with the semisimple algebras of the second rank with an arbitrary choice of the grading in them are presented in explicit form. General solution of such…

The general solution of two-dimensional matrix Toda chain equations with fixed ends

It is shown that the two-dimensional matrix Toda chain determines the group of discrete symmetries of the two-dimensional matrix nonlinear Schrödinger equation (the matrix generalization of the…

On the classification of real forms of non-Abelian Toda theories and W-algebras