[Structures d'algébres amassées généralisées sur le double de Drinfeld du group GLn]
We construct a generalized cluster structure compatible with the Poisson bracket on the Drinfeld double of the standard Poisson–Lie group
On construit des structures d'algèbres amassées généralisées compatibles avec le crochet de Poisson sur le double de Drinfeld du group
Accepté le :
Publié le :
Michael Gekhtman 1 ; Michael Shapiro 2 ; Alek Vainshtein 3
@article{CRMATH_2016__354_4_345_0, author = {Michael Gekhtman and Michael Shapiro and Alek Vainshtein}, title = {Generalized cluster structure on the {Drinfeld} double of {\protect\emph{GL}\protect\textsubscript{\protect\emph{n}}}}, journal = {Comptes Rendus. Math\'ematique}, pages = {345--349}, publisher = {Elsevier}, volume = {354}, number = {4}, year = {2016}, doi = {10.1016/j.crma.2016.01.006}, language = {en}, }
TY - JOUR AU - Michael Gekhtman AU - Michael Shapiro AU - Alek Vainshtein TI - Generalized cluster structure on the Drinfeld double of GLn JO - Comptes Rendus. Mathématique PY - 2016 SP - 345 EP - 349 VL - 354 IS - 4 PB - Elsevier DO - 10.1016/j.crma.2016.01.006 LA - en ID - CRMATH_2016__354_4_345_0 ER -
Michael Gekhtman; Michael Shapiro; Alek Vainshtein. Generalized cluster structure on the Drinfeld double of GLn. Comptes Rendus. Mathématique, Volume 354 (2016) no. 4, pp. 345-349. doi : 10.1016/j.crma.2016.01.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.01.006/
[1] Solutions of the classical Yang–Baxter equation for simple Lie algebras, Funkc. Anal. Prilozh., Volume 16 (1982), pp. 1-29
[2] Cluster algebras. III. Upper bounds and double Bruhat cells, Duke Math. J., Volume 126 (2005), pp. 1-52
[3] Cluster χ-varieties for dual Poisson–Lie groups. I, Algebra Anal., Volume 22 (2010), pp. 14-104
[4] Teichmüller spaces of Riemann surfaces with orbifold points of arbitrary order and cluster variables, Int. Math. Res. Not., Volume 2014 (2014) no. 10, pp. 2746-2772
[5] Cluster algebras and Poisson geometry, Mosc. Math. J., Volume 3 (2003), pp. 899-934
[6] Cluster Algebras and Poisson Geometry, Mathematical Surveys and Monographs, vol. 167, The American Mathematical Society, Providence, RI, USA, 2010
[7] Cluster structures on simple complex Lie groups and Belavin–Drinfeld classification, Mosc. Math. J., Volume 12 (2012), pp. 293-312
[8] Cremmer–Gervais cluster structure on
[9] Exotic cluster structures on
[10] Group-theoretical methods in the theory of finite-dimensional integrable systems, Encyclopaedia of Mathematical Sciences, vol. 16, Springer-Verlag, Berlin, 1994, pp. 116-225
- Cluster scattering diagrams and theta functions for reciprocal generalized cluster algebras, Annals of Combinatorics, Volume 27 (2023) no. 3, pp. 615-691 | DOI:10.1007/s00026-022-00623-1 | Zbl:1542.13017
- Periodic Staircase Matrices and Generalized Cluster Structures, International Mathematics Research Notices, Volume 2022 (2022) no. 6, p. 4181 | DOI:10.1093/imrn/rnaa148
- Generalized cluster structures related to the Drinfeld double of
, Journal of the London Mathematical Society. Second Series, Volume 105 (2022) no. 3, pp. 1601-1633 | DOI:10.1112/jlms.12542 | Zbl:1521.13033 - Linear relations for Laurent polynomials and lattice equations, Nonlinearity, Volume 33 (2020) no. 11, pp. 5961-5996 | DOI:10.1088/1361-6544/ab9dcc | Zbl:1468.13052
- A quantum analog of generalized cluster algebras, Algebras and Representation Theory, Volume 21 (2018) no. 6, pp. 1203-1217 | DOI:10.1007/s10468-017-9743-7 | Zbl:1408.16008
- Colliding holes in Riemann surfaces and quantum cluster algebras, Nonlinearity, Volume 31 (2018) no. 1, p. 54 | DOI:10.1088/1361-6544/aa9729
- Drinfeld double of
and generalized cluster structures, Proceedings of the London Mathematical Society. Third Series, Volume 116 (2018) no. 3, pp. 429-484 | DOI:10.1112/plms.12086 | Zbl:1432.53117 - Quantum groups, quantum tori, and the Grothendieck-Springer resolution, Advances in Mathematics, Volume 321 (2017), pp. 431-474 | DOI:10.1016/j.aim.2017.09.010 | Zbl:1419.17023
- Cluster algebras and semi-invariant rings. II: Projections, Mathematische Zeitschrift, Volume 285 (2017) no. 3-4, pp. 939-966 | DOI:10.1007/s00209-016-1733-7 | Zbl:1468.13050
Cité par 9 documents. Sources : Crossref, zbMATH
Commentaires - Politique