Families of algebraic structures

Dominique Manchon (U Clerment Auvergne)

Oct 13. 2020, 13:15 — 14:00

Algebraic structures may come into families, where each operation at hand is replaced by a family of operations indexed by some parameter set, which often bears a semigroup structure. The characteristic relations of the structure at stake (e.g. associativity relation, of Jacobi identity, of pre-Lie relation, etc.) persist together with a play on the parameters involving the semigroup structure. The first example, namely Rota-Baxter family algebras, comes from the momentum scheme in Quantum Field Theory.   I will introduce Rota-Baxter families, then address other family structures (dendriform, duplicial, pre-Lie,...), and finally give a general account of family algebras over a finitely presented linear operad, this operad together with its presentation naturally defining an algebraic structure on the set of parameters. Based on recent joint works with Loïc Foissy, Xing Gao and Yuanyuan Zhang.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Higher Structures Emerging from Renormalisation - partially postponed (Online Workshop)
Pierre Clavier (U of Haut-Alsace)
Kurusch Ebrahimi-Fard (NTNU, Trondheim)
Peter K. Friz (TU Berlin)
Harald Grosse (U of Vienna)
Dominique Manchon (U Clerment Auvergne)
Sylvie Paycha (U of Potsdam)
Sylke Pfeiffer (U of Potsdam)