幂等子代数上的支撑τ-倾斜模

The support τ-tilting modules over idempotent subalgebras

设A是数域k上的有限维代数, e是A中的幂等元.本文证明了,如果A/AeA是左投射A-模,则有限生成右eAe-模T是支撑τ-倾斜模当且仅当T■eAe eA是A上的支撑τ-倾斜模.另一方面,如果A是遗传代数, T是支撑τ-倾斜A-模, A/AeA是右投射A-模,则Hom_(A)(eA, T)是支撑τ-倾斜eAe-模.作为应用,本文证明了,若代数A是τ-倾斜有限的,则幂等子代数eAe也是τ-倾斜有限的.

Let A be a finite-dimensional k-algebra and e be an idempotent of A. In this paper, we show that if A/AeA is a projective left A-module, then a finitely generated right eAe-module T is a support τ-tilting module if and only if T ■ eAe eA is a support τ-tilting A-module. On the other hand, if A is a hereditary algebra, T is a support τ-tilting A-module and A/AeA is a projective right A-module, then Hom;(eA, T) is a support τ-tilting eAe-module. As an application, we prove that if A is τ-tilting finite, then eAe is also τ-tilting finite.