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Mat. Sb., 1998, Volume 189, Number 3, Pages 3–44 (Mi msb302)  

This article is cited in 1 scientific paper (total in 1 paper)

Canonical forms for the invariant tensors and $A$-$B$-$C$-cohomologies of integrable Hamiltonian systems

O. I. Bogoyavlenskii

Queen's University

Abstract: The canonical forms for the $(\ell ,m)$ tensors, $\ell +m\leqslant 3$, that are invariant with respect to a Liouville-integrable non-degenerate Hamiltonian system $V$ on a symplectic manifold $M^{2k}$ are derived. It is proved that the characteristic polynomial of any invariant $(1,1)$ tensor $A^\alpha _\beta$ is a perfect square; therefore its eigenvalues have even multiplicities. Any invariant metric $g_{\alpha \beta }$ is indefinite and has signature $\sigma \leqslant k$. The derived canonical forms are applied to the calculation of the $A$-$B$-$C$-cohomologies of Liouville-integrable Hamiltonian systems.

DOI: https://doi.org/10.4213/sm302

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English version:
Sbornik: Mathematics, 1998, 189:3, 315–357

Bibliographic databases:

UDC: 517.9
MSC: 58F07, 58A12
Received: 25.08.1997

Citation: O. I. Bogoyavlenskii, “Canonical forms for the invariant tensors and $A$-$B$-$C$-cohomologies of integrable Hamiltonian systems”, Mat. Sb., 189:3 (1998), 3–44; Sb. Math., 189:3 (1998), 315–357

Citation in format AMSBIB
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\by O.~I.~Bogoyavlenskii
\paper Canonical forms for the~invariant tensors and $A$-$B$-$C$-cohomologies of integrable Hamiltonian systems
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    This publication is cited in the following articles:
    1. Smirnov, RG, “The action-angle coordinates revisited: Bi-Hamiltonian systems”, Reports on Mathematical Physics, 44:1–2 (1999), 199  crossref  mathscinet  zmath  adsnasa  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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