On Centralizers of Belavin–Drinfeld r-Matrices
Анотація
У статтi наводиться структурний результат про централiзатори $r\textrm{-}$матриць Белавiна-Дрiнфельда. Цей результат є корисним для обчислення когомологiй Белавiна-Дрiнфельда, якi були введенi ранiше для класифiкацiї деяких бiалгебр Лi та квантових груп.
Mathematical Subject Classification 2020: 17B62, 17B37, 17B67, 20G10
Ключові слова:
Белавiн-Дрiнфельд, квантова група, бiалгебра ЛiПосилання
S. Alsaody and A. Pianzola, On the classification of Lie bialgebras by cohomological means, Doc. Math. 24 (2019), 2583--2612. https://doi.org/10.4171/dm/734
A. Belavin and V. Drinfeld, Triangle equations and simple Lie algebras, Soviet Sci. Rev. Sect. C: Math. Phys. Rev. 4 (1984), 93--165.
N. Bourbaki, Groupes et algèbres de Lie, Ch. 7 et 8, Hermann, 1975.
B. Kadets, E. Karolinsky, I. Pop, and A. Stolin, Quantum groups: from Kulish-Reshetikhin discovery to classification, Zapiski Nauchnykh Seminarov POMI 433 (2015), 186--195.
B. Kadets, E. Karolinsky, I. Pop, and A. Stolin, Classification of quantum groups and Belavin-Drinfeld cohomologies, Comm. Math. Phys. 344 (2016), 1--24. https://doi.org/10.1007/s00220-016-2622-y
B. Kadets, E. Karolinsky, I. Pop, and A. Stolin, Classification of quantum groups and Belavin-Drinfeld cohomologies for orthogonal and symplectic Lie algebras, J. Math. Phys. 57 (2016), Paper No. 051707. https://doi.org/10.1063/1.4950895
E. Karolinsky, A. Pianzola, and A. Stolin, Classification of quantum groups via Galois cohomology, Comm. Math. Phys. 377 (2020), 1099--1129. https://doi.org/10.1007/s00220-019-03597-z
A. Pianzola and A. Stolin, Belavin-Drinfeld solutions of the Yang-Baxter equation: Galois cohomology considerations, Bull. Math. Sciences 8 (2018), 1--14. https://doi.org/10.1007/s13373-016-0094-1
J.-P. Serre, Cohomologie Galoisienne, Springer, 1994. https://doi.org/10.1007/BFb0108758
A. Stolin and I. Pop, Classification of quantum groups and Lie bialgebra structures on sl(n, 𝔽). Relations with Brauer group, Adv. Math. 296 (2016), 324--342. https://doi.org/10.1016/j.aim.2016.02.002