4 papers · 1 filter
Monoidal Gröbner systems and categories of affine Brauer type
Sigiswald Barbier, Léo Schelstraete
We introduce an analogue of Gröbner bases, or equivalently, Bergman's diamond lemma, for linear (super)monoidal categories. It gives a systematic way to study monoidal ideals and t…
A basis and Schur-Weyl duality for the loop Hecke algebra
Geoffrey Janssens, Abel Lacabanne, Léo Schelstraete +1
The loop Hecke algebra is a generalization of the Hecke algebra to the loop braid group, introduced by Damiani, Martin and Rowell. We give a new presentation of the loop Hecke alge…
Rewriting modulo in diagrammatic algebras and application to categorification
Léo Schelstraete
We develop a rewriting theory modulo suitable for higher linear structures. In particular, the theory is suited for diagrammatic algebras as they appear in categorification, repres…
Odd Khovanov homology, higher representation theory and higher rewriting theory
Léo Schelstraete
This thesis is devoted to the fields of quantum topology and rewriting theory, and their surprising interconnections. In the first part of the thesis, we develop a higher represent…