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Let be an algebraically closed field. Let be a finite dimensional commutative local -algebra and let be a quiver with no oriented cycles. In this paper, we study (signed) -exceptional sequences over the algebra , which is isomorphic to . We show there is a bijection between the set of complete (signed) -exceptional sequences in and the set of complete (signed) -exceptional sequences in . Moreover, we prove that every -perpendicular subcategory of is equivalent to the module category of , for some quiver . As a consequence, we prove that the -cluster morphism categories of and are equivalent.

生成讲解博客的中文版本

生成AI智能校验的中文版本