16 citations · 43 across the 10 of their papers we have counts for
11 papers
A uniform construction of Chevalley normal forms for automorphic Lie algebras on the Riemann sphere
Vincent Knibbeler
For a finite subgroup of and one of its ground forms , we show that the space of invariants of degree $k\in2\mathbb{…
A classification of automorphic Lie algebras on complex tori
Vincent Knibbeler, Sara Lombardo, Casper Oelen
We classify the automorphic Lie algebras of equivariant maps from a complex torus to . For each case we compute a basis in a normal form. The automorph…
Computing equivariant matrices on homogeneous spaces for Geometric Deep Learning and Automorphic Lie Algebras
Vincent Knibbeler
We develop an elementary method to compute spaces of equivariant maps from a homogeneous space of a Lie group to a module of this group. The Lie group is not required to…
Polyhedral Groups in
Vincent Knibbeler, Sara Lombardo, Casper Oelen
We classify embeddings of the finite groups , and in the Lie group up to conjugation.
Wild Local Structures of Automorphic Lie Algebras
Drew Duffield, Vincent Knibbeler, Sara Lombardo
We study automorphic Lie algebras using a family of evaluation maps parametrised by the representations of the associative algebra of functions. This provides a descending chain of…
Automorphic Lie algebras and modular forms
V. Knibbeler, S. Lombardo, A. P. Veselov
We introduce and study certain hyperbolic versions of automorphic Lie algebras related to the modular group. Let be a finite index subgroup of with…
Automorphic Lie Algebras and Cohomology of Root Systems
Vincent Knibbeler, Sara Lombardo, Jan A. Sanders
A cohomology theory of root systems emerges naturally in the context of Automorphic Lie Algebras, where it helps formulating some structure theory questions. In particular, one can…
Hereditary Automorphic Lie Algebras
Vincent Knibbeler, Sara Lombardo, Jan A. Sanders
We show that Automorphic Lie Algebras which contain a Cartan subalgebra with a constant spectrum, called hereditary, are completely described by 2-cocycles on a classical root syst…
Higher dimensional Automorphic Lie Algebras
Vincent Knibbeler, Sara Lombardo, Jan A. Sanders
The paper presents the complete classification of Automorphic Lie Algebras based on , where the symmetry group is finite and the orbit is any of t…
Invariants of Automorphic Lie Algebras
Vincent Knibbeler
Automorphic Lie Algebras arise in the context of reduction groups introduced in the late 1970s in the field of integrable systems. They are subalgebras of Lie algebras over a ring…
The laminations of a crystal near an anti-continuum limit
Vincent Knibbeler, Blaz Mramor, Bob Rink
The anti-continuum limit of a monotone variational recurrence relation consists of a lattice of uncoupled particles in a periodic background. This limit supports many trivial equil…