Graded Lie algebras, representation theory, integrable mappings and systems

@article{Leznov1998GradedLA,
  title={Graded Lie algebras, representation theory, integrable mappings and systems},
  author={Andrey N. Leznov},
  journal={arXiv: Mathematical Physics},
  year={1998}
}
  • A. Leznov
  • Published 8 August 1998
  • Mathematics
  • arXiv: Mathematical Physics
View PDF on arXiv
8 Citations
Background Citations
2
Methods Citations
1

8 Citations

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…

W-algebras for non-abelian Toda systems

U V Manifold and Integrable Systems in Spaces of Arbitrary Dimension

Abstract The 2n dimensional manifold with two mutually commutative operators of differentiation is introduced. Nontrivial multidimensional integrable systems connected with arbitrary graded…

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

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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…

Planar pure braids on six strands

The group of planar (or flat) pure braids on $n$ strands, also known as the pure twin group, is the fundamental group of the configuration space $F_{n,3}(\mathbb{R})$ of $n$ labelled points in…

The MSSM fine tuning problem: a way out

As is well known, electroweak breaking in the MSSM requires substantial fine-tuning, mainly due to the smallness of the tree-level Higgs quartic coupling, λtree. Hence the fine tuning is efficiently…

Desperately seeking supersymmetry (SUSY)

The discovery of x-rays and radioactivity in the waning years of the 19th century led to one of the most awe-inspiring scientific eras in human history. The 20th century witnessed a level of…

References

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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…

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 new look on the theory of integrable systems

The solution of the N = (0|2) superconformal f-Toda lattice

Canonical transformations generated by shifts in nonlinear lattices

The integrable mapping as the discrete group of inner symmetry of integrable systems

Infinite dimensional Lie algebras: Frontmatter

The translationally non-invariant quantization of a generalized toda lattice

Graded algebras of the second rank and integration of nonlinear equations Yzz=exp (2Y)−2Y, Yzz=2 exp (Y)−exp (−2Y)

In the terms of the notions of the theory of infinite-dimensional algebras of finite growth of the second rank, we have derived solutions to the equations; Yzz=exp (2Y)−2Y, Yzz=2 exp (Y)−exp (−2Y)…

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…
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