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I've recently been trying to understand Hochschild and cyclic co/homology better, and I've noticed that while it's common to define the Hochschild homology $\mathrm{HH}_{\bullet}(A;M)$ of an $R$-...

A finite dimensional (connected if needed) $K$-algebra $A$ over a field $K$ is called symmetric when $A \cong Hom_K(A,K)$ as $A$-bimodules. Symmetric algebras are Frobenius algebras and include for ...

I am trying to understand Hochschild homology, in particular the Hochschild–Kostant–Rosenberg theorem. As far as I understand this result gives an isomorphism between the algebraic (Kähler) ...

According to this post Intuition for group homology, I wonder what is the intuition for Hochschild homology. The Hochschild homology is defined as the homology of this complex chain. Given a ...

Let $A$ be an associative unital $k$-algebra, and let $M$ be a bimodule of $A$. The Hochschild cohomology of $A$ with coefficients in $M$ can be defined as $$HH^{n}(A,\,M)=\mathrm{Ext}^{n}_{A^{e}}(A,\,...