Operations on the Hochschild Bicomplex of a Diagram of Algebras

TY - UNPB

T1 - Operations on the Hochschild Bicomplex of a Diagram of Algebras

AU - Hawkins, Eli

N1 - 60 pages

PY - 2020/2/3

Y1 - 2020/2/3

N2 - 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 asimplicial subcomplex and its cohomology. This structure governs deformations of diagrams of algebras through the Maurer-Cartan equation.

AB - 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 asimplicial subcomplex and its cohomology. This structure governs deformations of diagrams of algebras through the Maurer-Cartan equation.

KW - math.CT

KW - math.AT

KW - math.RA

KW - 18D50 (primary) 16E40 (Secondary)

UR - http://arxiv.org/abs/2002.00886

M3 - Working paper

BT - Operations on the Hochschild Bicomplex of a Diagram of Algebras

ER -