6 papers
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 local -action on odd Khovanov homology
Mark Ebert, Léo Schelstraete
We show that odd Khovanov homology carries an action of the super Lie algebra , given extra choice of markings on the link. Moreover, we show that this action…
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…
Odd Khovanov homology and higher representation theory
Léo Schelstraete, Pedro Vaz
We introduce a super analogue of -foams, and use it to define an invariant of oriented tangles, shown to coincide with odd Khovanov homology when restricted to lin…