An Application of a Theorem of Sheila Brenner for Hochschild Extension Algebras of a Truncated Quiver Algebra

Abstract

Let A be a truncated quiver algebra over an algebraically closed field such that any oriented cycle in the ordinary quiver of A is zero in A. We give the number of the indecomposable direct summands of the middle term of an almost split sequence for a class of Hochschild extension algebras of A by the standard duality module D(A).

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Acknowledgment

The author is grateful to Professor Katsunori Sanada and Doctor Tomohiro Itagaki for many helpful suggestions on improving the clarity of the article. Finally, I thank the referee for useful comments.

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Correspondence to Hideyuki Koie.

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Presented by: Henning Krause

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Koie, H. An Application of a Theorem of Sheila Brenner for Hochschild Extension Algebras of a Truncated Quiver Algebra. Algebr Represent Theor (2021). https://doi.org/10.1007/s10468-020-10018-6

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Keywords

  • Hochschild extension
  • Hochschild (co)homology
  • Trivial extension
  • Self-injective algebra
  • Almost split sequence
  • Quiver

Mathematics Subject Classification (2010)

  • 16E40
  • 16G20
  • 16G70