Maximally non-abelian Toda systems

Nuclear Physics B

Volumn 494, Issue 3, 1997, Pages 657-686

  Razumov, A V ^a   Saveliev, M V ^b  

^a INSTITUTE FOR HIGH ENERGY PHYSICS   (Russian Federation)

^b LABORATOIRE DE PHYSIQUE STATISTIQUE   (France)

Author keywords

Gradation; Lie algebra; Lie group; Non abelian Toda systems; Quasideterminant

Indexed keywords

EID: 0031575035     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(97)00183-1     Document Type: Article

References (17)

1. [1] A.N. Leznov and M.V. Saveliev, Group-theoretical methods for integration of non-linear dynamical systems (Birkhauser, Basel, 1992).
2. [2] A.V. Razumov and M.V. Saveliev, Differential geometry of Toda systems, Commun. Anal. Geom. 2 (1994) 461.
3. [3] A.V. Razumov and M.V. Saveliev, Lie algebras, geometry and Toda-type systems (Cambridge University Press, Cambridge, 1997).
4. [4] A.V. Razumov and M.V. Saveliev, Multidimensional Toda type systems, hep-th/9609031.
5. [5] V.V. Gorbatsevich, A.L. Onishchik and E.B. Vinberg, Lie groups and Lie algebras, 3. Encyclopaedia of math, sciences, Vol. 41 (Amer. Math. Soc., New York, 1994).
6. [6] J.E. Humphreys, Linear algebraic groups (Springer, New York, 1975).
7. [7] J. Dixmier, Algèbres enveloppantes (Gauthier-Villars, Paris, 1974).
8. [8] M. Goto and F.D. Grosshans, Semisimple Lie algebras (Marcel Dekker, New York, 1978).
9. [9] I.M, Gelfand and V.S. Retakh, Determinants of matrices over non-commutative rings, Funct. Anal. Appl. 25 (1991) 91.
10. [10] I.M. Gelfand and V.S. Retakh, A theory of non-commutative determinants and characteristic functions of graphs, Funct. Anal. Appl. 26 (1992) 1.
11. [11] A.N. Leznov and E.A. Yusbashjan, The general solution of two-dimensional Toda chain equations with fixed ends, Lett. Math. Phys. 35 (1995) 345.
12. [12] J.-L. Gervais and M.V. Saveliev, Black holes from non-abelian Toda theories, Phys. Lett. B 286 (1992) 271.
13. [13] A. Bilal, Non-abelian Toda theory: A completely integrable model for strings on a black hole background, Nucl. Phys. B 422 (1994) 258.
14. [14] I.M. Krichever, The periodic non-abelian Toda chain and its two-dimensional generalization, Russ. Math. Surv. 36(2) (1981) 82.
15. [15] J.H.H. Perk and H.W. Capel, Transverse correlations in the inhomogeneous one-dimensional XY model at infinite temperature, Physica A 92 (1978) 163.
16. [16] A.V, Mikhailov, The reduction problem and the inverse scattering method, Physica 3D (1981) 73.
17. [17] P. Etingof, I. Gelfand and V. Retakh, Factorization of differential operators, quasideterminants, and non-abelian Toda field equations, q-alg/9701008.