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Izvestiya: Mathematics, 2004, Volume 68, Issue 4, Pages 659–708
DOI: https://doi.org/10.1070/IM2004v068n04ABEH000495
(Mi im495)
 

This article is cited in 29 scientific papers (total in 29 papers)

A symplectic groupoid of triangular bilinear forms and the braid group

A. I. Bondal

Steklov Mathematical Institute, Russian Academy of Sciences
References:
Abstract: We construct a symplectic groupoid of triangular bilinear forms and establish a relation with the flag variety. We also study the induced Poisson structure and the centre of the corresponding algebroid.
Received: 12.01.2004
Bibliographic databases:
Document Type: Article
UDC: 514.7
Language: English
Original paper language: Russian
Citation: A. I. Bondal, “A symplectic groupoid of triangular bilinear forms and the braid group”, Izv. Math., 68:4 (2004), 659–708
Citation in format AMSBIB
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\by A.~I.~Bondal
\paper A~symplectic groupoid of triangular bilinear forms and the braid group
\jour Izv. Math.
\yr 2004
\vol 68
\issue 4
\pages 659--708
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Linking options:
  • https://www.mathnet.ru/eng/im495
  • https://doi.org/10.1070/IM2004v068n04ABEH000495
  • https://www.mathnet.ru/eng/im/v68/i4/p19
  • This publication is cited in the following 29 articles:
    1. I. S. Beldiev, “Group of Isometries of the Lattice $K_0(\mathbb P_n)$”, Math. Notes, 115:4 (2024), 506–519  mathnet  crossref  crossref  mathscinet
    2. Yu-Wei Fan, Junho Peter Whang, “Stokes matrices and exceptional isomorphisms”, Math. Ann., 2024  crossref
    3. Yudai Hateruma, Yoshiki Kaneko, “On some Lie-theoretic solutions of the tt*-Toda equations with integer Stokes data”, J. Phys. A: Math. Theor., 57:4 (2024), 045202  crossref
    4. Giordano Cotti, Boris A. Dubrovin, Davide Guzzetti, Lecture Notes in Mathematics, 2356, Helix Structures in Quantum Cohomology of Fano Varieties, 2024, 97  crossref
    5. Kazuhiro Hikami, “A Note on Double Affine Hecke Algebra for Skein Algebra on Twice-Punctured Torus”, Journal of Geometry and Physics, 2024, 105408  crossref
    6. A. V. Fonarev, “Dual exceptional collections on Lagrangian Grassmannians”, Sb. Math., 214:12 (2023), 1779–1800  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    7. L. O. Chekhov, “Cluster variables for affine Lie–Poisson systems”, Theoret. and Math. Phys., 217:3 (2023), 1987–2004  mathnet  crossref  crossref  mathscinet  adsnasa
    8. Leonid O. Chekhov, Michael Shapiro, “Log-Canonical Coordinates for Symplectic Groupoid and Cluster Algebras”, Int. Math. Res. Not. IMRN, 2023:11 (2023), 9565–9652  mathnet  crossref
    9. Bertola M., Tarricone S., “Stokes Manifolds and Cluster Algebras”, Commun. Math. Phys., 390:3 (2022), 1413–1457  crossref  mathscinet  isi  scopus
    10. L. O. Chekhov, M. Z. Shapiro, H. Shibo, “Roots of the characteristic equation for the symplectic groupoid”, Russian Math. Surveys, 77:3 (2022), 552–554  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    11. Giordano Cotti, Alexander Varchenko, “The $*$-Markov equation for Laurent polynomials”, Mosc. Math. J., 22:1 (2022), 1–68  mathnet  crossref  mathscinet
    12. Bertola M., Korotkin D., “Tau-Functions and Monodromy Symplectomorphisms”, Commun. Math. Phys., 388:1 (2021), 245–290  crossref  mathscinet  isi
    13. Ciccoli N., “Quantum Orbit Method in the Presence of Symmetries”, Symmetry-Basel, 13:4 (2021), 724  crossref  isi
    14. Giordano Cotti, Alexander Varchenko, Proceedings of Symposia in Pure Mathematics, 103.1, Integrability, Quantization, and Geometry, 2021, 101  crossref
    15. Harder A., Thompson A., “Pseudolattices, Del Pezzo Surfaces, and Lefschetz Fibrations”, Trans. Am. Math. Soc., 373:3 (2020), 2071–2104  crossref  mathscinet  isi
    16. Sanda F. Shamoto Y., “An Analogue of Dubrovin'S Conjecture”, Ann. Inst. Fourier, 70:2 (2020), 621–682  crossref  mathscinet  isi
    17. 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
    18. Philip Boalch, “Geometry and braiding of Stokes data; Fission and wild character varieties”, Ann. Math, 179:1 (2014), 301  crossref  mathscinet  isi  scopus
    19. Leonid Chekhov, Marta Mazzocco, “Poisson Algebras of Block-Upper-Triangular Bilinear Forms and Braid Group Action”, Commun. Math. Phys, 2013  crossref  mathscinet  isi  scopus
    20. Massuyeau G., Oancea A., Salamon D.A., “Lefschetz Fibrations, Intersection Numbers, and Representations of the Framed Braid Group”, Bull. Math. Soc. Sci. Math. Roum., 56:4 (2013), 435–486  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:1233
    Russian version PDF:560
    English version PDF:91
    References:114
    First page:1
     
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