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TMF, 2018, Volume 196, Number 1, Pages 22–29 (Mi tmf9564)  

Cartan matrices in the Toda–Darboux chain theory

A. B. Shabat, V. E. Adler

Landau Institute for Theoretical Physics, Chernogolovka, Moscow Oblast, Russia

Abstract: We discuss a one-to-one correspondence between the polynomial first integrals of Hamiltonian systems with exponential interaction and the hyperintegrals of the two-dimensional Toda lattice. We establish formulas for recalculating the corresponding polynomials and some general properties of their algebraic structure.

Keywords: Cartan matrix, polynomial first integral, exponential system.

DOI: https://doi.org/10.4213/tmf9564

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English version:
Theoretical and Mathematical Physics, 2018, 196:1, 957–964

Bibliographic databases:

Received: 07.03.2018

Citation: A. B. Shabat, V. E. Adler, “Cartan matrices in the Toda–Darboux chain theory”, TMF, 196:1 (2018), 22–29; Theoret. and Math. Phys., 196:1 (2018), 957–964

Citation in format AMSBIB
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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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