대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제58권1호
  • /
  • Pages.183-193
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  • 2021
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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SEMIBRICKS OVER SPLIT-BY-NILPOTENT EXTENSIONS

  • Gao, Hanpeng (Department of Mathematics Nanjing University)
  • 투고 : 2020.02.29
  • 심사 : 2020.07.09
  • 발행 : 2021.01.31
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초록

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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참고문헌

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