Operations on the Hochschild Bicomplex of a Diagram of Algebras

Abstract

A diagram of algebras is a functor valued in a category of associative algebras. I construct an operad acting on the Hochschild bicomplex of a diagram of algebras. Using this operad, I give a direct proof that the Hochschild cohomology of a diagram of algebras is a Gerstenhaber algebra. I also show that the total complex is an $L_{\infty }$-algebra. The same results are true for the reduced and asimplicial subcomplexes and asimplicial cohomology. This structure governs deformations of diagrams of algebras through the Maurer-Cartan equation.

65 pages. Version 3: Published version. Minor corrections and improvements. I have changed "normalized'' to "reduced'' in order to be consistent with the literature

References in corpus (4)

• The L_\infty-deformation complex of diagrams of algebras
• Operads up to Homotopy and Deformations of Operad Maps
• Operadic structure on the Gerstenhaber-Schack complex for prestacks
• An A-infinity operad in spineless cacti

Cited by in corpus (1)

• Operadic structure on the Gerstenhaber-Schack complex for prestacks