Renormalization of chiral nuclear forces with multiple subtractions in peripheral channels

We analyse the renormalization of the of two-nucleon interaction with multiple subtractions in peripheral waves considering two chiral forces at N3LO. Phase shifts at low energies are then computed with several subtraction points below \mu = 10 / fm. We show that for most peripheral waves the phase shifts have nearly no dependence on the renormalization scale. In two cases the phase shifts converge slowly as the renormalization scale approaches \mu = 1 / fm and in one case the phase shifts presented oscillations with respect to the subtraction point \mu.Comment: 21 pages, 12 figures, to appear in the special issue "Few-Body Systems in High Energy Physics" (AHEP

Dilations of partial representations of Hopf algebras

We introduce the notion of a dilation for a partial representation (i.e. a partial module) of a Hopf algebra, which in case the partial representation origins from a partial action (i.e.a partial module algebra) coincides with the enveloping action (or globalization). This construction leads to categorical equivalences between the category of partial $H$-modules, a category of (global) $H$-modules endowed with a projection satisfying a suitable commutation relation and the category of modules over a (global) smash product constructed upon $H$, from which we deduce the structure of a Hopfish algebra on this smash product. These equivalences are used to study the interactions between partial and global representation theory.Comment: 25 pages. Corrected several typos, final version to appear in Journal of the London Mathematical Societ