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The Grassmann algebra in arbitrary characteristic and generalized signстатья
- Авторы: Dor Gal, Kanel-Belov Alexei, Vishne Uzi
- Журнал: ArXiv e-prints
- Год издания: 2015
- Первая страница: 25
- Аннотация: We define a generalization $G$ of the Grassmann algebra G which is well-behaved over arbitrary commutative rings $C$, even when 2 is not invertible. In particular, this enables us to define a notion of superalgebras that does not become degenerate in such a setting. Using this construction we are able to provide a basis of the non-graded multilinear identities of the free superalgebra with supertrace, valid over any ring. We also show that all identities of G follow from the Grassmann identity, and explicitly give its co-modules, which turn out to be generalizations of the sign representation. In particular, we show that the co-module is a free $C$-module of rank $2^{n−1}$
- Добавил в систему: Белов Алексей Яковлевич
Прикрепленные файлы
| № | Имя | Описание | Имя файла | Размер | Добавлен |
|---|---|---|---|---|---|
| 1. | Полный текст | 1501.02464v1.pdf | 301,6 КБ | 15 апреля 2016 [AlexeiBelov] |