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The Hochschild cohomology ring modulo nilpotence of a stacked monomial algebra

100%

Green E., Snashall N.

Colloquium Mathematicum

2006

tom 105

nr 2

233-258

This paper studies the Hochschild cohomology of finite-dimensional monomial algebras. If Λ = K𝓠/I with I an admissible monomial ideal, then we give sufficient conditions for the existence of an embedding of $K[x₁,..., x_r]/⟨x_ax_b for a ≠ b⟩$ into the Hochschild cohomology ring HH*(Λ). We also introduce stacked algebras, a new class of monomial algebras which includes Koszul and D-Koszul monomial algebras. If Λ is a stacked algebra, we prove that $HH*(Λ)/𝓝 ≅ K[x₁,..., x_r]/⟨x_ax_b for a ≠ b⟩$, where 𝓝 is the ideal in HH*(Λ) generated by the homogeneous nilpotent elements. In particular, this shows that the Hochschild cohomology ring of Λ modulo nilpotence is finitely generated as an algebra.

Hochschild cohomology of socle deformations of a class of Koszul self-injective algebras

100%

Snashall N., Taillefer R.

Colloquium Mathematicum

2010

tom 119

nr 1

79-93

We consider the socle deformations arising from formal deformations of a class of Koszul self-injective special biserial algebras which occur in the study of the Drinfeld double of the generalized Taft algebras. We show, for these deformations, that the Hochschild cohomology ring modulo nilpotence is a finitely generated commutative algebra of Krull dimension 2.

Ograniczanie wyników

2 Colloquium Mathematicum

2 Snashall N.

1 Green E.

1 Taillefer R.

1 2010

1 2006

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The Hochschild cohomology ring modulo nilpotence of a stacked monomial algebra

Hochschild cohomology of socle deformations of a class of Koszul self-injective algebras