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Mat. Sb., 2003, Volume 194, Number 7, Pages 155–160 (Mi msb757)  

This article is cited in 6 scientific papers (total in 6 papers)

Uniqueness of liftings of maximal commutative subalgebras of the Poisson–Lie algebra to the enveloping algebra

A. A. Tarasov

M. V. Lomonosov Moscow State University

Abstract: It is proved that each generalized Mishchenko–Fomenko subalgebra of the Poisson algebra of the Lie algebra ${{\mathfrak{gl}}_n({\mathbb C})}$ can be lifted to a unique commutative subalgebra of the enveloping algebra.

DOI: https://doi.org/10.4213/sm757

Full text: PDF file (227 kB)
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English version:
Sbornik: Mathematics, 2003, 194:7, 1105–1111

Bibliographic databases:

UDC: 519.46
MSC: 17B35, 17B63
Received: 20.01.2003

Citation: A. A. Tarasov, “Uniqueness of liftings of maximal commutative subalgebras of the Poisson–Lie algebra to the enveloping algebra”, Mat. Sb., 194:7 (2003), 155–160; Sb. Math., 194:7 (2003), 1105–1111

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. L. G. Rybnikov, “Centralizers of certain quadratic elements in Poisson–Lie algebras and the method of translation of invariants”, Russian Math. Surveys, 60:2 (2005), 367–369  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. L. G. Rybnikov, “The Argument Shift Method and the Gaudin Model”, Funct. Anal. Appl., 40:3 (2006), 188–199  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. Mishchenko S.P., Petrogradsky V.M., Regev A., “Poisson PI algebras”, Trans. Amer. Math. Soc., 359:10 (2007), 4669–4694  crossref  mathscinet  zmath  isi  elib  scopus
    4. Chervov A., Falqui G., Rybnikov L, “Limits of Gaudin Algebras, Quantization of Bending Flows, Jucys-Murphy Elements and Gelfand-Tsetlin Bases”, Letters in Mathematical Physics, 91:2 (2010), 129–150  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    5. Ilin A., Rybnikov L., “Degeneration of Bethe Subalgebras in the Yangian of Gl(N)”, Lett. Math. Phys., 108:4 (2018), 1083–1107  crossref  mathscinet  zmath  isi  scopus
    6. Molev A., Yakimova O., “Quantisation and Nilpotent Limits of Mishchenko-Fomenko Subalgebras”, Represent. Theory, 23 (2019), 350–378  crossref  mathscinet  zmath  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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