arXiv Open Access 2020

Derived Representation Type and Field Extensions

Jie Li Chao Zhang

Lihat Sumber

Abstrak

Let $A$ be a finite-dimensional algebra over a field $k$. We define $A$ to be $\mathbf{C}$-dichotomic if it has the dichotomy property of the representation type on complexes of projective $A$-modules. $\mathbf{C}$-dichotomy implies the dichotomy properties of representation type on the levels of homotopy category and derived category. If $k$ admits a finite separable field extension $K/k$ such that $K$ is algebraically closed, the real number field for example, we prove that $A$ is $\mathbf{C}$-dichotomic. As a consequence, the second derived Brauer-Thrall type theorem holds for $A$, i.e., $A$ is either derived discrete or strongly derived unbounded.

Topik & Kata Kunci

math.RT

Penulis (2)

Jie Li

Chao Zhang

Format Sitasi

APA MLA BibTeX

Li, J., Zhang, C. (2020). Derived Representation Type and Field Extensions. https://arxiv.org/abs/2003.08589

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2020
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓