We establish the conjugacy of Cartan subalgebras for extended affine Lie algebras whose centreless core is “of type A”, i.e., ℓ×ℓ-matrices over a quantum torus Q whose trace lies in the commutator space of Q. This settles ...

In this work, we show that an n-dimensional sublattice Λ′ = mΛ of an n-dimensional lattice Λ induces a G = Znm tessellation in the flat torus Tβ′ = Rn/Λ′, where the group G is isomorphic to the lattice partition Λ/Λ′ . As ...

The study of entanglement spectra is a powerful tool to detect or elucidate universal behavior in quantum many-body systems. We investigate the scaling of the entanglement (or Schmidt) gap δξ , i.e., the lowest-laying gap ...

We study relevant features of the spectrum of the quantum open baker map. The opening consists of a cut along the momentum p direction of the 2-torus phase space, modeling an open chaotic cavity. We study briefly the ...

We study 2-cocycle twists, or equivalently Zhang twists, of semigroup algebras over a field k. If the underlying semigroup is affine, that is abelian, cancellative and finitely generated, then Spec k[S] is an affine toric ...

We study the oscillations of a scalar field on a noncommutative disc implementing the boundary as the limit case of an interaction with an appropriately chosen confining background. The space of quantum fluctuations of the ...