Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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SEMIBRICKS OVER SPLIT-BY-NILPOTENT EXTENSIONS

  • Gao, Hanpeng (Department of Mathematics Nanjing University)
  • Received : 2020.02.29
  • Accepted : 2020.07.09
  • Published : 2021.01.31
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Abstract

In this paper, we prove that there is a bijection between the ��-tilting modules and the sincere left finite semibricks. We also construct (sincere) semibricks over split-by-nilpotent extensions. More precisely, let �� be a split-by-nilpotent extension of a finite-dimensional algebra �� by a nilpotent bimodule ��E��, and �� ⊆ mod ��. We prove that �� ⊗�� �� is a (sincere) semibrick in mod �� if and only if �� is a semibrick in mod �� and Hom��(��, �� ⊗�� E) = 0 (and �� ∪ �� ⊗�� E is sincere). As an application, we can construct ��-tilting modules and support ��-tilting modules over ��-tilting finite cluster-tilted algebras.

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References

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