On the Decomposition of the Hochschild Cohomology Group of a Monomial Algebra Satisfying a Separability Condition

Ayako Itaba, Takahiko Furuya, Katsunori Sanada

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In this paper, we consider the finite connected quiver Q having two subquivers Q (1)and Q (2)with (Formula presented.). Suppose that Q (i)is not a subquiver of Q (j)where {i, j} = {1, 2}. For a monomial algebra Λ =kQ/I obtained by the quiver Q, when the associated sequence of paths given by Minsharp <(I) satisfies a certain separability condition, we propose the method so that we easily construct a minimal projective resolution of Λ as a right Λe-module and calculate the Hochschild cohomology group of Λ.

Original languageEnglish
Pages (from-to)2282-2292
Number of pages11
JournalCommunications in Algebra
Issue number6
Publication statusPublished - 3 Jun 2015



  • Associated sequence of path
  • Hochschild cohomology
  • Monomial algebra
  • Path algebra

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