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Mosc. Math. J., 2004, том 4, номер 3, страницы 627–654 (Mi mmj167)  

Эта публикация цитируется в 126 научных статьях (всего в 126 статьях)

Finite tensor categories

[Конечные тензорные категории]

P. Etingof, V. V. Ostrik

Department of Mathematics, Massachusetts Institute of Technology

Аннотация: Мы развиваем общую структурную теорию конечных тензорных категорий (возможно неполупростых), обобщая результаты в полупростом случае, недавно полученные в нашей совместной работе с Д. Никшичем. В частности, мы обобщаем на категорный случай теоремы о свободе для алгебр Хопфа и квазихопфовых алгебр, принадлежащие Николсу–Золлер и Шауенбургу соответственно. Мы также приводим категорные версии теории выделенных группоподобных элементов в конечномерных алгебрах Хопфа, результата Лоренца о вырожденности матрицы Картана и теоремы об отсутствии примитивных элементов в конечномерных алгебрах Хопфа над полями нулевой характеристики. Мы развиваем теорию модульных категорий и двойственных категорий для возможно неполупростых конечных тензорных категорий; в частности, мы вводим новое понятие точной модульной категории. Наконец, мы классифицируем неразложимые точные модульные категории над простейшими конечными тензорными категориями, такими как представления конечных групп в положительной характеристике, представления конечных супергрупп, представления алгебры Тафта.

DOI: https://doi.org/10.17323/1609-4514-2004-4-3-627-654

Полный текст: http://www.ams.org/.../abst4-3-2004.html
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MSC: 18D10
Статья поступила: 27 марта 2003 г.
Язык публикации: английский

Образец цитирования: P. Etingof, V. V. Ostrik, “Finite tensor categories”, Mosc. Math. J., 4:3 (2004), 627–654

Цитирование в формате AMSBIB
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\paper Finite tensor categories
\jour Mosc. Math.~J.
\yr 2004
\vol 4
\issue 3
\pages 627--654
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