On B∞-algebra structures

Maria Immaculada Gálvez Carrillo (UPC, Barcelona)

Apr 28. 2023, 12:15 — 13:00

A B∞-algebra is an algebraic structure encoding higher multibraces and homotopy associativity, first encountered by Baues in relation to iterated loop spaces. More famous is the example of a B∞ structure on the Hochschild cochain complex: the relation of B∞ to G∞ algebras was crucial for some proofs of Deligne's Hochschild cohomology conjecture.

We present work in progress (joint with M Ronco and A Tonks) investigating the appearance of canonical B∞-algebra structures on any algebra endowed with an independent differential graded algebra structure.

A special case of a commutative analogue of this is the appearance of Koszul's L∞ brace hierarchy, of importance in the BRST approach to closed string theory. Other special cases we rely on are due to Börjeson, Markl and Loday-Ronco.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Non-commutative Geometry meets Topological Recursion (Workshop)
Gaëtan Borot (HU Berlin)
Elba Garcia Failde (Sorbonne U, Paris)
Harald Grosse (U of Vienna)
Masoud Khalkhali (Western U, Ontario)
Hannah Markwig (U Tübingen)
Raimar Wulkenhaar (U Münster)