Abstract
Let k be the algebraic closure of a finite field q and A be a finite dimensional k-algebra with a Frobenius morphism F. In the present paper we establish a relation between the stable module category of the repetitive algebra  of A and that of the repetitive algebra of the fixed-point algebra A F. As an application, it is shown that the derived category of A F is equivalent to the subcategory of F-stable objects in the derived category of A when A has a finite global dimension.
| Original language | English |
|---|---|
| Pages (from-to) | 169-184 |
| Number of pages | 16 |
| Journal | Science in China, Series A: Mathematics |
| Volume | 51 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Feb 2008 |
| Externally published | Yes |
Keywords
- Derived category
- Frobenius morphism
- Repetitive algebra
- Stable module category
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Deng, B., & Wan, J. (2008). Frobenius morphisms and stable module categories of repetitive algebras. Science in China, Series A: Mathematics, 51(2), 169-184. https://doi.org/10.1007/s11425-007-0152-y