Quantum automorphisms of matroids

Abstract: Motivated by the vast literature of quantum automorphism groups of graphs, we define and study quantum automorphism groups of matroids. A key feature of quantum groups is that there are many quantizations of a classical group, and this phenomenon manifests in the cryptomorphic characterizations of matroids. Our primary goals are to understand, using theoretical and computational techniques, the relationship between these quantum groups and to find when these quantum groups exhibit quantum symmetry. Finally, we prove a matroidal analog of Lovász's theorem characterizing graph isomorphisms in terms of homomorphism counts.

Joint work with Daniel Corey, Julien Schanz, Marcel Wack, and Moritz Weber.

machine learningcommutative algebraalgebraic geometryalgebraic topologycombinatoricscategory theoryoperator algebrasrings and algebrasrepresentation theory

Audience: researchers in the topic

( chat )

---

Algebraic and Combinatorial Perspectives in the Mathematical Sciences

Series comments: To receive announcements: Register into our mailing list by going to our main website www.math.ntnu.no/acpms/

---