Generalized cluster structures related to the Drinfeld double of GLn

Misha Gekhtman, Michael Shapiro, Alek Vainshtein

نتاج البحث: نشر في مجلةمقالةمراجعة النظراء

ملخص

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.

اللغة الأصليةإنجليزيّة أمريكيّة
الصفحات (من إلى)1601-1633
عدد الصفحات33
دوريةJournal of the London Mathematical Society
مستوى الصوت105
رقم الإصدار3
المعرِّفات الرقمية للأشياء
حالة النشرنُشِر - أبريل 2022

All Science Journal Classification (ASJC) codes

  • !!General Mathematics

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