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Hilbert series of PI relatively free G-graded algebras are rational functionsстатья
- Авторы: Kanel–Belov A., Aljadeff Eli
- Журнал: ArXiv e-prints
- Номер: 1011.3253
- Год издания: 2010
- Аннотация: Let G be a finite group, (g_{1},...,g_{r}) an (unordered) r-tuple of G^{(r)} and x_{i,g_i}'s variables that correspond to the g_i's, i=1,...,r. Let F<x_{1,g_1},...,x_{r,g_r}> be the corresponding free G-graded algebra where F is a field of zero characteristic. Here the degree of a monomial is determined by the product of the indices in G. Let I be a G-graded T-ideal of F<x_{1,g_1},...,x_{r,g_r}> which is PI (e.g. any ideal of identities of a G-graded finite dimensional algebra is of this type). We prove that the Hilbert series of F<x_{1,g_1},...,x_{r,g_r}>/I is a rational function. More generally, we show that the Hilbert series which corresponds to any g-homogeneous component of F<x_{1,g_1},...,x_{r,g_r}>/I is a rational function.
- Добавил в систему: Белов Алексей Яковлевич
Прикрепленные файлы
| № | Имя | Описание | Имя файла | Размер | Добавлен |
|---|---|---|---|---|---|
| 1. | Полный текст | 1011.3253v1.pdf | 212,8 КБ | 16 апреля 2016 [AlexeiBelov] |