We study homological properties of a family of algebras called toupie algebras. Our main objective is to obtain the Gerstenhaber structure of their Hochschild cohomology, with the purpose of describing the Lie algebra structure of the first Hochschild cohomology space, together with the Lie module structure of the whole Hochschild cohomology.

中文翻译：

---

Toupie代数的Hochschild同调的Gerstenhaber结构

我们研究称为toupie代数的代数族的同源性。我们的主要目的是获得其Hochschild同调性的Gerstenhaber结构，以描述第一个Hochschild同调空间的Lie代数结构，以及整个Hochschild同调性的Lie模结构。