Operations on the Hochschild bicomplex of a diagram of algebras

Eli Hawkins (UCAS)

Aug 27. 2020, 15:30 -- 16:30

Motivated by algebraic quantum field theory, I consider diagrams of algebras, i.e., functors valued in a category of associative algebras. Deformations of a diagram of algebras satisfy cubic relations and thus are not described by the quadratic Maurer-Cartan equation in a differential graded Lie algebra – suggesting the presence of an L-infinity algebra.

I describe a (differential graded) operad, Quilt, that encodes useful operations on the Hochschild bicomplex of a diagram of vector spaces. The Quilt operations generalize the brace operations for a single vector space. 

Quilt extends to another operad, mQuilt, that acts on the Hochschild bicomplex of a diagram of algebras. This allows an explicit proof that the Hochschild cohomology of a diagram of algebras is a Gerstenhaber algebra.

Further Information
Where:
ESI Boltzmann Lecture Hall
Associated Event:
Higher Structures and Field Theory (Thematic Programme)
Organizer(s):
Anton Alekseev (U Genève)
Stefan Fredenhagen (U Vienna)
Nicolai Reshetikhin (UC, Berkeley)
Thomas Strobl (U Lyon)
Chenchang Zhu (U Göttingen)