The Tamarkin--Tsygan calculus of an algebra a la Stasheff

Abstract

We show how to compute the Tamarkin-Tsygan calculus of an associative algebra by providing, for a given cofibrant replacement of it, a `small' ${\mathsf{Calc}}_{\infty }$-model of its calculus, which we make somewhat explicit at the level of $\mathsf{Calc}$-algebras. To do this, we prove that the operad $\mathsf{Calc}$ is inhomogeneous Koszul; to our best knowledge, this result is new. We illustrate our technique by carrying out some computations for two monomial associative algebra using the cofibrant replacement obtained by the author in 1804.01435.

Final version. Available at publisher's website

References in corpus (5)

• Formality of the homotopy calculus algebra of Hochschild (co)chains
• A little bit of extra functoriality for Ext and the computation of the Gerstenhaber bracket
• Derived invariance of the cap product in Hochschild theory
• Endofunctors and Poincaré-Birkhoff-Witt theorems
• Minimal models for monomial algebras