TY - JOUR
T1 - Generalized cluster structures related to the Drinfeld double of GLn
AU - Gekhtman, Misha
AU - Shapiro, Michael
AU - Vainshtein, Alek
N1 - Publisher Copyright: © 2022 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.
PY - 2022/4
Y1 - 2022/4
N2 - We prove that the regular generalized cluster structure on the Drinfeld double of (Formula presented.) constructed in Gekhtman, Shapiro, and Vainshtein (Int. Math. Res. Notes, 2022, to appear, arXiv:1912.00453) is complete and compatible with the standard Poisson–Lie structure on the double. Moreover, we show that for (Formula presented.) this structure is distinct from a previously known regular generalized cluster structure on the Drinfeld double, even though they have the same compatible Poisson structure and the same collection of frozen variables. Further, we prove that the regular generalized cluster structure on band periodic matrices constructed in Gekhtman, Shapiro, and Vainshtein (Int. Math. Res. Notes, 2022, to appear, arXiv:1912.00453) possesses similar compatibility and completeness properties.
AB - We prove that the regular generalized cluster structure on the Drinfeld double of (Formula presented.) constructed in Gekhtman, Shapiro, and Vainshtein (Int. Math. Res. Notes, 2022, to appear, arXiv:1912.00453) is complete and compatible with the standard Poisson–Lie structure on the double. Moreover, we show that for (Formula presented.) this structure is distinct from a previously known regular generalized cluster structure on the Drinfeld double, even though they have the same compatible Poisson structure and the same collection of frozen variables. Further, we prove that the regular generalized cluster structure on band periodic matrices constructed in Gekhtman, Shapiro, and Vainshtein (Int. Math. Res. Notes, 2022, to appear, arXiv:1912.00453) possesses similar compatibility and completeness properties.
UR - http://www.scopus.com/inward/record.url?scp=85124970363&partnerID=8YFLogxK
U2 - 10.1112/jlms.12542
DO - 10.1112/jlms.12542
M3 - Article
SN - 0024-6107
VL - 105
SP - 1601
EP - 1633
JO - Journal of the London Mathematical Society
JF - Journal of the London Mathematical Society
IS - 3
ER -