Abstract

Let B be the one-point extension algebra of A by an A-module X. We proved that every support τ-tilting A-module can be extended to be a support τ-tilting B-module by two different ways. As a consequence, it is shown that there is an inequality $$|\mathrm{s}\tau ‐\text{tilt\hspace{0.17em}}\mathrm{\hspace{0.17em}}B|⩾2|\mathrm{s}\tau ‐\text{tilt\hspace{0.17em}}A|.$$

中文翻译：

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一站式扩展支持τ倾斜模块

摘要

设B为A的A-模块X的单点扩展代数。我们证明，可以通过两种不同的方式将每个支持τ倾斜A模块扩展为支持τ倾斜B模块。结果表明存在不平等$$|\mathrm{s}\tau ‐\text{倾斜\hspace{0.17em}}\mathrm{\hspace{0.17em}}乙|⩾2|\mathrm{s}\tau ‐\text{倾斜\hspace{0.17em}}\mathrm{一个}|。$$