When using the Born–Oppenheimer approximation for molecular systems, one encounters a quantum mechanical Hamiltonian for the electrons that depends on several parameters that describe the positions of the nuclei. As these parameters are varied, the spectrum of the electron Hamiltonian may vary. In particular, discrete eigenvalues may approach very close to one another at “avoided crossings” of ...

We classify the cosemisimple Hopf algebras whose corepresentation semi-ring is isomorphic to that of GL(2). This leads us to define a new family of Hopf algebras which generalize the quantum similitude group of a non-degenerate bilinear form. A detailed study of these Hopf algebras gives us an isomorphic classification and the description of their corepresentation categories.

IfH is a Hopf algebra whose square of the antipode is the identity, v ∈ L(V )⊗H is a corepresentation, and π : H → L(W ) is a representation, then u = (id ⊗ π)v satisfies the equation (t ⊗ id)u = ((t ⊗ id)u) of the vertex models for subfactors. A universal construction shows that any solution u of this equation arises in this way. A more elaborate construction shows that there exists a “minimal...

The observable algebra O of SOq(3)-symmetric quantum mechanics is generated by the coordinates Pi and Xi of momentum and position spaces (which are both isomorphic to the SOq(3)-covariant real quantum space IR 3 q). Their interrelations are determined with the quantum group covariant differential calculus. For a quantum mechanical representation of O on a Hilbert space essential self-adjointnes...

Let k be an algebraically closed field. The main goal of this paper is to classify the finite-dimensional pointed Hopf algebras over k of finite corepresentation type. To do so, we give a necessary and sufficient condition for a basic Hopf algebra over k to be of finite representation type firstly. Explicitly, we prove that a basic Hopf algebra over k is of finite representation type if and onl...

By giving an interesting characterisation of amenable multiplicative unitaries, we show in a simple way that bicrossproducts of amenable locally compact groups is both amenable and coamenable. Amenability of Kac algebras has been studied in [3]. In [1], amenability of regular multiplicative unitaries was also defined. Recently, we studied in [7] and [9] amenable Hopf C *-algebras and amenable K...

We present explicit examples finite tensor categories that are C2-graded extensions of the corepresentation category of certain finite-dimensional non-semisimple Hopf algebras. Mathematics Subject Classification (2010): 18D10, 16W30, 19D23.

In human-human interactions, corepresenting a partner's actions is crucial to successfully adjust and coordinate actions with others. Current research suggests that action corepresentation is restricted to interactions between human agents facilitating social interaction with conspecifics. In this study, we investigated whether action corepresentation, as measured by the social Simon effect (SS...