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The Hochschild cohomology is a tool for studying associative algebras that has a lot of structure: it is a Gerstenhaber algebra. However, computing this structure is difficult. We will give a mild introduction to this cohomology, we will justify its importance by computing some of the lower degrees, and we will emphasize the limitations of restricting ourselves to one resolution. We will conclude by presenting some of the recent developments that advance the understanding of its structure, and by mentioning applications to quantum symmetries.

	Notes 239 KB application/pdf
	Slides 1.67 MB application/pdf

Structures in Hochschild cohomology