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arXiv · 1403.6375

Hochschild cohomology for a class of some self-injective special biserial algebras of rank four

Takahiko Furuya
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Abstract

In this paper, we construct an explicit minimal projective bimodule resolution of a self-injective special biserial algebra $A_{T}$ ($T\geq0$) whose Grothendieck group is of rank $4$. As a main result, we determine the dimension of the Hochschild cohomology group ${\rm HH}^{i}(A_{T})$ of $A_{T}$ for $i\geq0$, completely. Moreover we give a presentation of the Hochschild cohomology ring modulo nilpotence ${\rm HH}^{*}(A_{T})/\mathcal{N}_{A_{T}}$ of $A_{T}$ by generators and relations in the case where $T=0$.

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Takahiko Furuya. 2014-03-25. Hochschild cohomology for a class of some self-injective special biserial algebras of rank four. https://arxiv.org/abs/1403.6375

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