TY - JOUR
T1 - On integrability of transverse Lie–Poisson structures at nilpotent elements
AU - Dinar, Yassir
N1 - Funding Information:
A part of this work was done during the author visits to the Abdus Salam International Centre for Theoretical Physics (ICTP) and the International School for Advanced Studies (SISSA) through the years 2014–2017. This work was also funded by the internal grants of Sultan Qaboos University, Oman (IG/SCI/DOMS/15/04) and (IG/SCI/DOMS/19/08). The author likes to thank anonymous reviewers for critically reading the manuscript and suggesting substantial improvements.
Publisher Copyright:
© 2020 Elsevier B.V.
PY - 2020/9
Y1 - 2020/9
N2 - We construct families of functions in involution for transverse Poisson structures at nilpotent elements of Lie–Poisson structures on simple Lie algebras by using the argument shift method. Examples show that these families contain completely integrable systems that consist of polynomial functions. We provide a uniform construction of these integrable systems for an infinite family of distinguished nilpotent elements of semisimple type.
AB - We construct families of functions in involution for transverse Poisson structures at nilpotent elements of Lie–Poisson structures on simple Lie algebras by using the argument shift method. Examples show that these families contain completely integrable systems that consist of polynomial functions. We provide a uniform construction of these integrable systems for an infinite family of distinguished nilpotent elements of semisimple type.
KW - Argument shift method
KW - Completely integrable system
KW - Finite W-algebra
KW - Nilpotent elements of semisimple type
KW - Polynomial Poisson brackets
KW - Slodowy slice
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U2 - 10.1016/j.geomphys.2020.103690
DO - 10.1016/j.geomphys.2020.103690
M3 - Article
AN - SCOPUS:85085348841
SN - 0393-0440
VL - 155
JO - Journal of Geometry and Physics
JF - Journal of Geometry and Physics
M1 - 103690
ER -