Classical and quantum Kneser graphs

Preprint Sep 2026

Schrijver-Delsarte rigidity in association schemes and undecidability of quantum graph homomorphism

We prove RE-completeness of the quantum homomorphism problem parameterised by families of graphs derived from the classic metric association schemes. These include Kneser graphs, $q$-Kneser graphs, and the complements of Johnson, Grassmann, and Hamming graphs. Our proof develops a spectral method for establishing non-c...

Lorenzo Ciardo, Iris Hebbeker, Gideo Joubert et al. · 0 citations

Preprint Sep 2026

On the exact quantum chromatic number of generalized Johnson graphs

This paper investigates the quantum chromatic number of generalized Johnson graphs and determines the exact quantum chromatic numbers of two infinite families of generalized Johnson graphs, which exhibit an exponential separation between the classical and quantum chromatic numbers.

Gao-Jun Luo, Xi-Wang Cao, Shi-Tao Li et al. · 0 citations

Preprint Oct 2026

The Quantum Cayley Graphs of the Kac-Paljutkin Quantum Group

We study the quantum Cayley graphs associated with the Kac-Paljutkin quantum group. We determine which projections give rise to undirected, irreflexive and connected quantum graphs and classify them up to isomorphism. Their spectra and chromatic numbers are computed. For the special case of the projection $p = I_2$ we...

Luca Junk · 0 citations

Preprint Aug 2026

Local quantum Cuntz--Krieger algebras of dephasing quantum graphs

We establish a general structure theorem for local quantum Cuntz--Krieger families associated to finite quantum graphs whose relations are analogous to those of the partial isometries generating an ordinary graph $C^*$-algebra, with the quantum edge correspondence governing composition. We apply this structure theorem...

Lara Ismert · 0 citations

Preprint Oct 2026

Operator Algebraic Quantum Hypergroups

We develop a theory of operator algebraic quantum hypergroups and their representations, formulated using a special case of the algebraic quantum hypergroup framework of van Daele and Delvaux. As part of the axioms, every operator algebraic quantum hypergroup admits a dual object of the same type. We prove that a certa...

Benjamin Anderson-Sackaney, L. Vainerman · 0 citations

Review Open access Oct 2026

Homological properties of quantum generalized Heisenberg algebras

This paper presents a survey of several classes of Heisenberg-type algebras, including classical, quantum, and generalized variants. We examine the relationships between different families, such as quantum Heisenberg algebras, generalized Heisenberg algebras, quantum generalized Heisenberg algebras, Ore extensions an...

S. A. Lopes, Héctor Suárez, Yésica Suárez · Beiträge zur Algebra und Geo... · 1 citation · ⚡1