c-vectors via τ-tilting theory
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- 作者：Changjian Fu changjianfu@scu.edu.cn
- 关键词：τ-rigid module ; c-vectors ; Cluster algebra ; Sign-coherence ; Tropical dualities ; Quasitilted algebra
- 刊名：Journal of Algebra
- 出版年：2017
- 出版时间：1 March 2017
- 年：2017
- 卷：473
- 期：Complete
- 页码：194-220
- 全文大小：541 K
- 卷排序：473
文摘
Inspired by the tropical dualities in cluster algebras, we introduce c-vectors for finite-dimensional algebras via τ-tilting theory. Let A be a finite-dimensional algebra over an algebraically closed field k. Each c-vector of A can be realized as the (negative) dimension vector of certain indecomposable A-module and hence we establish the sign-coherence property for this kind of c-vectors. We then study the positive c-vectors for certain classes of finite-dimensional algebras including quasitilted algebras and cluster-tilted algebras. In particular, we recover the equalities of c-vectors for acyclic cluster algebras and skew-symmetric cluster algebras of finite type respectively obtained by Nájera Chávez. To this end, a short proof for the sign-coherence of c-vectors for skew-symmetric cluster algebras has been given in the appendix.