Hochschild cohomology and dominant dimension

A new approach is established to compare Hochschild cohomologies of an algebra and of its centralizer subalgebras. This approach is based on dominant dimension, a homological dimension that is shown to control the comparison in a precise sense for a large class of algebras including classical and quantized Schur algebras. For the same class of algebras, it is shown that derived equivalences preserve dominant dimension. This is applied to determine the dominant dimensions of qq-Schur algebras and of their blocks.