# Higher dimensional generalizations of the Thompson groups via higher rank graphs

@article{Lawson2020HigherDG, title={Higher dimensional generalizations of the Thompson groups via higher rank graphs}, author={Mark V. Lawson and Aidan Sims and Alina Vdovina}, journal={arXiv: Group Theory}, year={2020} }

We construct a family of groups from suitable higher rank graphs which are analogues of the finite symmetric groups. We introduce homological invariants showing that many of our groups are, for example, not isomorphic to $nV$, when $n \geq 2$.

## 6 Citations

### A GENERALISATION OF HIGHER-RANK GRAPHS

- MathematicsBulletin of the Australian Mathematical Society
- 2021

Abstract We introduce ‘generalised higher-rank k-graphs’ as a class of categories equipped with a notion of size. They extend not only higher-rank k-graphs, but also the Levi categories introduced by…

### HIGHER RANK GRAPHS FROM CUBE COMPLEXES AND THEIR SPECTRAL THEORY

- Mathematics
- 2021

We propose constructions of k-graphs from combinatorial input and initiate a study of their spectral theory. Guided by geometric insight, we obtain several new series of k-graphs using cube complexes…

### C*-algebras of higher-rank graphs from groups acting on buildings, and explicit computation of their K-theory.

- Mathematics
- 2020

We unite elements of category theory, K-theory, and geometric group theory, by defining a class of groups called $k$-cube groups, which act freely and transitively on the product of $k$ trees, for…

### Higher dimensional digraphs from cube complexes and their spectral theory

- Mathematics
- 2021

. We deﬁne k -dimensional digraphs and initiate a study of their spectral theory. The k -dimensional digraphs can be viewed as generating graphs for small categories called k -graphs. Guided by…

### The Polycyclic Inverse Monoids and the Thompson Groups Revisited

- MathematicsSemigroups, Categories, and Partial Algebras
- 2021

We revisit our construction of the Thompson groups from the polycyclic inverse monoids in the light of new research. Specifically, we prove that the Thompson group $G_{n,1}$ is the group of units of…

### Higman–Thompson‐like groups of higher rank graph C*‐algebras

- MathematicsBulletin of the London Mathematical Society
- 2022

Let Λ$\Lambda$ be a row‐finite and source‐free higher rank graph with finitely many vertices. In this paper, we define the Higman–Thompson‐like group Λht$\operatorname{\Lambda _{ht}}$ of the graph…

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