2026/2027
Квантовые группы 1
ID 1249572
Статус:
Дисциплина общефакультетского пула
Кто читает:
Факультет математики
Где читается:
Факультет математики
Когда читается:
1, 2 модуль
Охват аудитории:
для всех кампусов НИУ ВШЭ
Язык:
английский
Кредиты:
6
Контактные часы:
60
Course Syllabus
Abstract
"Quantum groups have been a fundamental tool for specialists in mathematical physics and representation theory for several decades. On one hand, quantum groups are deformations of universal enveloping Lie algebras such that the representation category remains tensor category; on the other hand, they are quantizations of the algebras of functions on a Lie group (hence the name). Standard examples of applications of quantum groups include: construction of bases in representations of semisimple Lie algebras, studying quantum integrals of motion for various physical models, obtaining knot invariants. The representation theory of quantum groups is very interesting to study: on one hand, many statements from the representation theory of usual Lie algebras can be transfered to the case of quantum groups; on the other, new effects arise, such as existence of non-semisimple finite-dimensional representations when the quantization parameter is a root of unity, as well as the combinatorics of the crystall limit.
""Quantum Groups I"" is the first part of a year-long course on quantum groups. A continuation, ""Quantum Groups II,"" is planned for the spring semester. In the fall semester, we will begin with general facts about Lie bialgebras and their quantization, and then focus on the quantization of universal enveloping finite-dimensional Lie algebras and their representations."
Expected Learning Outcomes
- Понимание базовых свойств алгебр Хопфа
- Задание квантовой универсальной обёртывающей образующими и соотношениями
