Семейные алгебры (мини-курс)

Мини-курс будет состоять из четырех лекций (11, 15, 18 и 22 декабря - это понедельники и пятницы).

Кроме того, А.А.Кириллов сделает доклад на семинаре Э.Б.Винберга в МГУ 20 декабря.

Preliminaries for the course (in English)

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Preliminary exercises (in English)

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A new class of associative algebras (so-called family algebras) is introduced and investigated. These algebras are related to an irreducible representation of a simple complex Lie algebra. A family algebra is a sort of a finite approximation to the enveloping algebra $U(\g)$ viewed as a module over its center.

It turns out that several important questions about semi-simple algebras and their representations can be formulated, studied and sometimes solved in terms of family algebras.

Here we only start this program and hope that it will be continued and developed.

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