In this talk, we 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 $\Phi$ of natural numbers, the $\Phi$-Beilinson-Green algebras $\scr G^{\Phi}_A(X)$ and $\scr G^{\Phi_B(N\otimes_AX)$ are stably equivalent of Morita type. In particular, if $\Phi=\{0\}$, 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.
会议ID:370 6440 2914
会议密码:123456
潘升勇,博士毕业于北京师范大学,研究方向为代数表示论;现为北京交通大学理学院副教授;在 J. Algebra、 Math. Nachr.、J. Pure Appl. Algebra等杂志上发表10余篇论文;主持多项国家自然科学基金委项目。