We introduce and study certain hyperbolic versions of automorphic Lie algebras related to the modular group. Let $\Gamma$ be a finite index subgroup $\mathrm{SL}(2,\mathbb{Z})$ with an action on complex simple algebra $\mathfrak g$, which can extended $\mathrm{SL}(2,\mathbb{C})$. show that corresponding $\mathfrak{g}$-valued forms is isomorphic extension $\mathfrak{g}$ over usual forms. This es...

We characterize the space of the so-called planar mixed automorphic forms of type (ν, μ) with respect to an equivariant pair (ρ, τ) as the image of the usual automorphic forms by an appropriate transform and we investigate some concrete basic spectral properties of a magnetic Schrödinger operator acting on them. The associated polynomials constitute classes of generalized complex polynomials of...

The cohomology of an arithmetic group is built out of certain automorphic forms. This allows computational investigation of these automorphic forms using topological techniques. We discuss recent techniques developed for the explicit computation of the cohomology of congruence subgroups of GL2 over CM-quartic and complex cubic number fields as Hecke-modules.