The main focus of this paper is to present a method to construct new stable equivalences of Morita type. Suppose that a B‐A‐bimodule N define a stable equivalence of Morita type between finite dimensional algebras A and B. Then, for any generator X of the A‐module category and any finite admissible set Φ of natural numbers, the Φ‐Beilinson–Green algebras ${\mathcal{G}}_A^{\mathrm{\Phi }}(X)$ and ${\mathcal{G}}_B^{\mathrm{\Phi }}\left(N{\otimes }_{A}X\right)$ are stably equivalent of Morita type. In particular, if $\mathrm{\Phi }=\{0\}$, we get a known result in literature. As another consequence, we construct an infinite family of derived equivalent algebras of the same dimension and of the same dominant dimension such that they are pairwise not stably equivalent of Morita type. Finally, we develop some techniques for proving that, if there is a graded stable equivalence of Morita type between graded algebras, then we can get a stable equivalence of Morita type between Beilinson–Green algebras associated with graded algebras.

中文翻译：

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Φ‐Beilinson–Green代数的Morita型的稳定等价

本文的主要重点是提出一种构造森田类型新的稳定等价物的方法。假设B ‐ A‐ Bimodule N定义了有限维代数A和B之间的Morita类型的稳定等价。然后，对于任何发电机X中的甲-module类别和自然数的任何有限容许集Φ，Φ的-贝林松绿代数${\mathcal{G}}_{\mathrm{一种}}^{\mathrm{\Phi }}（X）$ 和 ${\mathcal{G}}_{乙}^{\mathrm{\Phi }}（ñ{\otimes }_{\mathrm{一种}}X）$稳定地等同于森田类型。特别是如果$\mathrm{\Phi }=\{0\}$，我们在文献中得到了一个已知的结果。另一个结果是，我们构造了一个无限族，它们具有相同维和相同主导维度的等价代数，以使它们成对地不稳定地等于Morita类型。最后，我们开发了一些技术来证明，如果在分级代数之间存在森田类型的分级稳定等价，那么我们就可以在与分级代数相关的贝林森-格林代数之间获得森田类型的稳定等价。