τ-Tilting theory and τ-slices

JOURNAL OF ALGEBRA

卷:481

Article

关键词: Representation theory;    Noncornmutative algebra;    Artinian algebras;    tau-Tilting theory;    Tilting theory;    Tilted algebras;    Cluster tilted algebras;   

DOI  :  10.1016/j.jalgebra.2017.03.004

来源: Elsevier

【 摘 要 】

Comparing the module categories of an algebra and of the endomorphism algebra of a given support tau-tilting module, we give a generalization of the Brenner Butler's tilting theorem in the framework of tau-tilting theory. Afterwards we define tau-slices and prove that complete slices of tilted algebras and local slices of cluster tilted algebras are examples of complete tau-slices. Then we apply this concept to the study of simply connected tilted algebras. Finally, we study the one-point extensions and the split-by-nilpotent extensions of an algebra with tau-slices. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free