Finite-dimensional integrable systems: A collection of research problems

A. V. Bolsinov; A. M. Izosimov; D. M. Tsonev

doi:10.1016/j.geomphys.2016.11.003

Finite-dimensional integrable systems: A collection of research problems

A. V. Bolsinov
, A. M. Izosimov
, D. M. Tsonev

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

This article suggests a series of problems related to various algebraic and geometric aspects of integrability. They reflect some recent developments in the theory of finite-dimensional integrable systems such as bi-Poisson linear algebra, Jordan–Kronecker invariants of finite dimensional Lie algebras, the interplay between singularities of Lagrangian fibrations and compatible Poisson brackets, and new techniques in projective geometry.

Original language	English (US)
Pages (from-to)	2-15
Number of pages	14
Journal	Journal of Geometry and Physics
Volume	115
DOIs	https://doi.org/10.1016/j.geomphys.2016.11.003
State	Published - May 1 2017
Externally published	Yes

Keywords

Bi-Poisson algebra
Bi-Poisson geometry
Compatible Poisson brackets
Jordan–Kronecker invariants

ASJC Scopus subject areas

Mathematical Physics
General Physics and Astronomy
Geometry and Topology

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10.1016/j.geomphys.2016.11.003

Cite this

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title = "Finite-dimensional integrable systems: A collection of research problems",

abstract = "This article suggests a series of problems related to various algebraic and geometric aspects of integrability. They reflect some recent developments in the theory of finite-dimensional integrable systems such as bi-Poisson linear algebra, Jordan–Kronecker invariants of finite dimensional Lie algebras, the interplay between singularities of Lagrangian fibrations and compatible Poisson brackets, and new techniques in projective geometry.",

keywords = "Bi-Poisson algebra, Bi-Poisson geometry, Compatible Poisson brackets, Jordan–Kronecker invariants",

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AU - Tsonev, D. M.

PY - 2017/5/1

Y1 - 2017/5/1

N2 - This article suggests a series of problems related to various algebraic and geometric aspects of integrability. They reflect some recent developments in the theory of finite-dimensional integrable systems such as bi-Poisson linear algebra, Jordan–Kronecker invariants of finite dimensional Lie algebras, the interplay between singularities of Lagrangian fibrations and compatible Poisson brackets, and new techniques in projective geometry.

AB - This article suggests a series of problems related to various algebraic and geometric aspects of integrability. They reflect some recent developments in the theory of finite-dimensional integrable systems such as bi-Poisson linear algebra, Jordan–Kronecker invariants of finite dimensional Lie algebras, the interplay between singularities of Lagrangian fibrations and compatible Poisson brackets, and new techniques in projective geometry.

KW - Bi-Poisson algebra

KW - Bi-Poisson geometry

KW - Compatible Poisson brackets

KW - Jordan–Kronecker invariants

UR - https://www.scopus.com/pages/publications/85028258474

UR - https://www.scopus.com/pages/publications/85028258474#tab=citedBy

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SP - 2

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JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

ER -

Finite-dimensional integrable systems: A collection of research problems

Abstract

Keywords

ASJC Scopus subject areas

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