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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2004, Volume 246, Pages 43–63 (Mi tm145)  
This article is cited in 5 scientific papers (total in 5 papers)

Symplectic Groupoids Related to Poisson–Lie Groups

A. I. Bondal

Steklov Mathematical Institute, Russian Academy of Sciences
Full-text PDF (282 kB) Citations (5)
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Abstract: A new interpretation of a groupoid of triangular bilinear forms is given. Namely, we construct a symplectic groupoid related to any given Poisson–Lie group with an appropriate involution. This allows one to construct a symplectic groupoid dual to the groupoid of triangular forms.
Received in February 2004
Bibliographic databases:
Document Type: Article
UDC: 512.7
Language: Russian
Citation: A. I. Bondal, “Symplectic Groupoids Related to Poisson–Lie Groups”, Algebraic geometry: Methods, relations, and applications, Collected papers. Dedicated to the memory of Andrei Nikolaevich Tyurin, corresponding member of the Russian Academy of Sciences, Trudy Mat. Inst. Steklova, 246, Nauka, MAIK «Nauka/Inteperiodika», M., 2004, 43–63; Proc. Steklov Inst. Math., 246 (2004), 34–53
Citation in format AMSBIB
\Bibitem{Bon04}
\by A.~I.~Bondal
\paper Symplectic Groupoids Related to Poisson--Lie Groups
\inbook Algebraic geometry: Methods, relations, and applications
\bookinfo Collected papers. Dedicated to the memory of Andrei Nikolaevich Tyurin, corresponding member of the Russian Academy of Sciences
\serial Trudy Mat. Inst. Steklova
\yr 2004
\vol 246
\pages 43--63
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm145}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2101283}
\zmath{https://zbmath.org/?q=an:1181.17010}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2004
\vol 246
\pages 34--53
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  • https://www.mathnet.ru/eng/tm145
  • https://www.mathnet.ru/eng/tm/v246/p43
    • This publication is cited in the following 5 articles:
    1. L. O. Chekhov, M. Mazzocco, “On a Poisson homogeneous space of bilinear forms with a Poisson–Lie action”, Russian Math. Surveys, 72:6 (2017), 1109–1156  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Fock V.V., Goncharov A.B., “The quantum dilogarithm and representations of quantum cluster varieties”, Invent. Math., 175:2 (2009), 223–286  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. Molev A.I., Ragoucy E., “Symmetries and invariants of twisted quantum algebras and associated Poisson algebras”, Rev. Math. Phys., 20:2 (2008), 173–198  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    4. Li Luen-Chau, “Poisson involutions, spin Calogero–Moser systems associated with symmetric Lie subalgebras and the symmetric space spin Ruijsenaars–Schneider models”, Comm. Math. Phys., 265:2 (2006), 333–372  crossref  mathscinet  zmath  adsnasa  isi  scopus
    5. A. I. Bondal, “A symplectic groupoid of triangular bilinear forms and the braid group”, Izv. Math., 68:4 (2004), 659–708  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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