We show that the secondary Hochschild cohomology associated to a triple $(A,B, epsilon)$ has several of the properties of the usual Hochschild cohomology. Among others, we prove that the total secondary Hochschild complex is a multiplicative nonsymmetric operad, discuss the connection with extensions of $B$-algebras, and give a Hodge-type decomposition of the secondary Hochschild cohomology.
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机译：我们表明，与三元$（A，B， epsilon）$相关的次要Hochschild同调具有通常Hochschild同调的一些特性。其中，我们证明了总的次级Hochschild复数是一个可乘的非对称运算，讨论了与$ B $-代数扩展的联系，并给出了次级Hochschild同调的Hodge型分解。
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