Деформационное квантование и квантовые группы. Лекция 8, Г.И.Шарыгин, А.Б.Жеглов
07.04.26 Докладчик: Mikhail Chirkov (HSE and YarSU) Quantisation ideals and canonical parametrisations of the unipotent group Abstract: The method of quantisation ideals for dynamical systems on the free associative algebra was introduced by A.V. Mikhailov in 2020 as an alternative approach to the problem of quantisation. In our joint work with A.V. Mikhailov and D.V. Talalaev, we generalize this approach to the case of discrete dynamics on the free associative algebra A. This dynamics is defined by a well-known solution of the Zamolodchikov tetrahedron equation, which is related to the problem of re-parameterisation of the unipotent group N(3, A). As a result, we construct several families of quantisations, analyze their classical limit and obtain canonical integrable systems compatible with re-parameterisations. In the first half of the talk I will provide a brief overview of the history and motivation behind the approach of quantisation ideals. In the second half I will describe our construction and some additional ideas. Лекторы - Георгий Игоревич Шарыгин, Александр Борисович Жеглов Страница курса - https://mccme.ru/ru/nmu/courses-of-nmu/vesna-20252026/s26-sem-sharygin/ Плейлист на YouTube - https://www.youtube.com/playlist?list=PLp9ABVh6_x4HOc2v9JY66I5XgnFjdxui0 Плейлист на RuTube - https://rutube.ru/plst/1460187 Канал НМУ на RuTube - https://rutube.ru/channel/42881756/
07.04.26 Докладчик: Mikhail Chirkov (HSE and YarSU) Quantisation ideals and canonical parametrisations of the unipotent group Abstract: The method of quantisation ideals for dynamical systems on the free associative algebra was introduced by A.V. Mikhailov in 2020 as an alternative approach to the problem of quantisation. In our joint work with A.V. Mikhailov and D.V. Talalaev, we generalize this approach to the case of discrete dynamics on the free associative algebra A. This dynamics is defined by a well-known solution of the Zamolodchikov tetrahedron equation, which is related to the problem of re-parameterisation of the unipotent group N(3, A). As a result, we construct several families of quantisations, analyze their classical limit and obtain canonical integrable systems compatible with re-parameterisations. In the first half of the talk I will provide a brief overview of the history and motivation behind the approach of quantisation ideals. In the second half I will describe our construction and some additional ideas. Лекторы - Георгий Игоревич Шарыгин, Александр Борисович Жеглов Страница курса - https://mccme.ru/ru/nmu/courses-of-nmu/vesna-20252026/s26-sem-sharygin/ Плейлист на YouTube - https://www.youtube.com/playlist?list=PLp9ABVh6_x4HOc2v9JY66I5XgnFjdxui0 Плейлист на RuTube - https://rutube.ru/plst/1460187 Канал НМУ на RuTube - https://rutube.ru/channel/42881756/