Hochschild cup product
= Hochschild cup product
{c}
{title2=$\smile$}
For $f\in C^p(A,A)$ and $g\in C^q(A,A)$, set $(f\smile g)(a_1,\ldots,a_{p+q})=f(a_1,\ldots,a_p)g(a_{p+1},\ldots,a_{p+q})$. This associative cochain multiplication descends to <Hochschild cohomology>, where it gives a <graded commutative algebra>. It is one operation in the <Gerstenhaber algebra> structure.