Hochschild cohomology and dominant dimension

Fang, Ming; Miyachi, Hyohe

doi:10.1090/tran/7704

Hochschild cohomology and dominant dimension
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by Ming Fang and Hyohe Miyachi PDF

Trans. Amer. Math. Soc. 371 (2019), 5267-5292 Request permission

Abstract:

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 $q$-Schur algebras and of their blocks.

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